Ratio, Proportion and Percentage
Q-1. A property dealer purchased house in Rs. 565000 and sold it for Rs. 525000 in the following year.
How much profit or loss did he make?
Q-2. A book seller received Rs. 18000 as commission at the rate of 15% for selling a particular book. The
list price of the book is Rs. 50. Find number of copy sold by the book seller and the total value of his sales.
Q-3. A dozen of egg was sold for Rs. 16. This figure included a profit of 17.5%. Find the cost.
Q-4. A dealer of house hold equipment paid Rs. 200000 for 15 refrigerators. He sold 2/5 of them at Rs. 15000 each and remainder at Rs. 14000 each. What was his Percent Profit?
Q-5. The compound interest for 2 years at 3.5 % on a sum of money exceeds the simple interest on it for the same time and same rate by Rs. 60.48. Find the principal.
Q-6. In a factory 25 power looms working 12 hours a day can provide 10800 meters cloth in 9 days.
How many power looms will produce 15552 meter cloth by working 9 hours in 12 days.
Q-7. A firm is increased his assets by 22.5% as compared to previous years assets. If the value of the firm is Rs. 545760. find the value of the firm’s assets in previous year.
Q-8. A chair that cost Rs. 137.5 is sold for Rs. 250. Find percentage of profit.
Q-9. 50 men working 8 hours a day can complete a building in 35 days. How many hours a day 70 men work to complete the same work in 25 days.
Q-10. A man paid Rs. 555 for a radio set after 7.5 % discount had been deducted. What was the market price of the set?
Q-11. Last month a stores sales were Rs. 25000 and this month the sales are Rs. 45230. Find out the percentage increase.
Q-12. Ali, Mohsin and Asghar are partners in a firm. Ali contributes ½ of capital for the whole year, Mohsin contributes ¼ of capital for 6 months. Asghar provide 1/5 of capital for 3 months. What is the share o f partners in profit of Rs. 25, 545.
Q-13. Three partners invested Rs. 18000, Rs. 16500 and Rs. 12500 respectively. If the third partners got Rs. 4625 as profit what was:
i. The total profit ii. Profit o f Ist and 2nd parents.
Q-14. A is half as old as B and B is half as old as C. The sum of their ages I is 105 years. Calculate the ages of A , B and C.
Q-15. A profit of Rs. 500000 is earned form business by four partners. This profit is to be allocated to the four partners in the ratio 4/5: 1/8: 2/3: 4 / 7.Determine the amount of profit of each partner.
Q-16. Mr. Khan , Mr. Furqan and Mr. Touseef are three partners they earned a profit of Rs. 18000. The profit can be shared in the ratio
Mr. Khan : Mr. Furqan = 2 : 5 and Mr. Furqan : Mr. Touseef 10 : 4
Find share of each partner in profit.
Q-17 An army formation of 900 men has a food stock for 30 days. Later on, 150 men leave the formation. Find for how many days the same food be sufficient for the remaining army men.
Q-18 Some quantity of rice is sufficient for 198 persons at the rate of 1/6 Kg per person. For how may persons the same quantity of rice be sufficient if each person is given 1/8 Kg of rice?
Q. 19. A building was constructed by three contractors. Contractor A employed 24 men for 10 days, contactor B employed 12 men for 15 days and Contractor C employed 15 men for 20 days. The men where paid Rs. 88400. How much did each contractor pay and what was the share of each men.
Q- 20. On a cut price shop, the price of a pair of shoes was Rs. 350 Which is 30% less of the actual price. Find the original price.
Q-21. A and B are in partnership. A gets as double as B`s profit. If A gets Rs. 4600 as profit then find what will B get? What is the total profit and ratio between the profits?
Q-22. A property agent sold a plot in
Q-23. An agent earned Rs. 27000 in commission at the rate of 4.5 % for selling a running departmental store. What was the selling price of the store?
Q-24. If the ratio of cars to trucks in a parking lot is 7 to 2 & there are 26 trucks, how many cars are there?
Q-25. A loaded truck of N.L.C. is of weight 7500 Kg. If 85% of this represents the load, how much is the truck weight?
Q-26. The estimated cost of a certain product was 12000 rupees but the actual expenditure exceeded it by Rs. 3600. Find the percentage increase in expenditure.
Q-27. If by the increase of 16 % the basic salary, of a Government employees will become Rs. 3248 p.m. What is his salary before the increase.
Q-28. A man spends 96% of his income and save Rs 525. What is his income?
Q-29. A photo-state machine operator purchased 20 packets of paper. The market price of a packet is Rs. 144 he get a discount of 17.5% & an additional 5% for cash. How much did he pay for the whole quantity?
Q- 30. A broker received Rs. 16000 for selling a price of land. His rate of commission was 2.5 %. What was the selling price?
Q-31. Ten tin of ghee was sold for Rs. 4025. Each tin contained 17.5 Kg ghee. The total selling price included the profit of 9.5%. Find the cost of ghee per kg.
Q-32. A watch was sold for Rs. 850 on 1.5 % loss. Find the cost price of the watch.
Q-34. A car dealer sold a car for Rs. 120,000 which he purchased fro Rs. 129000. Find his percentage gain or loss.
Q-33. A girl spend ¼ of her money on bus-fare and 2/3 of the remainder on drinks. What fraction of her original money was?
Q-34. In an election there were two candidates one of them received 65% of the votes cast and secured a majority of 1500 votes more than his competitor. How many people coasted the votes.
Q-35. The weight of Mangoes sold by three hawkers are in the ratio 3 : 4 : 5 . The least amount sold by one of them is 105 Kg. What is the amount of the mangoes sold by each of the other two hawkers.
Q-36. In a certain college there are 240 girls and 360 boys
i. What is the ratio of the number of girls to the number of boys.
ii. . /what is the ratio of the number of girls to the number of pupils.
Q-37. Three partners invested Rs. 18000. Rs. 16500 and Rs. 12500 respectively. When profit was distributed, the third one got Rs. 4625. Find the total profit earned.
Q- 38. Find the cost price if sales price = Rs. 140, Loss = 20%.
Q- 39. If 1/5 of an amount is Rs. 10,000, Find the amount.
Q-40. The estate of a person is valued at Rs. 600,000. His Bank over draft is Rs. 100,000.
His widow has 1/8 share in property. Remaining amount is to be divided
between two sons and one daughter. The share of son is double than daughter.
Q-41. A Company pays 4% out of profit to workers as bonus. The employees received
bonus of Rs 23500. What is total profit earned by the company.
Q-42. A chair has list price of Rs. 520. A trade discount of 20 percent is given to the
retailers. What is the cost to the retailers?
Q-43. A quality control inspector checks 100 shirts and finds 8 defective shirts out of them. How many shirts will be defective if 3000 shirts are checked?
Q.-44. The estate of deceased person consists of a house worth Rs. 200,000. Shop valued Rs. 150,000 and a car valued Rs. 80,000. He owed Rs. 50,000 to bank. The widow claimed 1/8 of property. The remaining property is shared between son and daughter in ratio of 2:1. What is the share of each?
Q-45. A bank lend Rs. 12,50,000 for two years. On ¾ of it bank charged 4 % interest, on the balance bank charged 5% interest. What is the amount of total interest that should charge by the bank?
Q-46. At what rate Rs. 5000 double itself in 5 Years.
Q-47. How long will it take to earn Rs. 11250 interest on a deposit of Rs. 75000 at 7.5% ?
Q-48. A man needs to borrow Rs. 30,000 for two years. Which of the following loan is more advantageous to him:
A. 4.1 % simple interest; or
B. 4% per annum compounded sem-annually.
Q- 49. A man borrowed Rs. 100,000 at 6% simple interest and invested the same amount at 6% compounded quarterly. What he gain after 5 years.
Q-50. The capital of a business grows @ 12% per annum compounded quarterly. If present capital is Rs. 300,000, what will be the capital after 3 years.
Q-51. How many annual payments of Rs. 1000 each are made in from of an ordinary annuity amounting to Rs. 13180.0 @ 6% p.a.
Q-52. A father of a girl planned to save some amount monthly to meet the marriage expenditure of his girl. Who is now 16 years of age? The father foresight marriage of his girls at the age of 21 years with an amount of Rs. 2,00,000. If the money grow at the rate of 12% p.a. compounded monthly then find how much amount he has to save each month.
S= Rs, 2,00,000 , n = 21 years – 15 years = 6 years = 6 x 12 months = 72 , I = 12% p.a. 12/12 = 0.01
Model Paper FBISE 2007
Section- A
(Marks: 16)
Q-1. Following table shows area and population of four provinces of
| Province | Area (Sp. Kilometer) | Population (000) | Ratio of Population to Area |
| | 347190 | 6566 | |
| NWFP | 74521 | 17744 | |
| | 205345 | 73621 | |
| SINDH | 140914 | 30440 | |
A. Calculate the ratio of population to area for each province and write it in your answer book.
B. If this ratio is called population density, which of the four provinces has the greatest population density?
Q- 2. It is known that 5 people produce 13kg of garbage in one.
Q-3. This is an incomplete table. Redraw this table in your answer book. Write the appropriate figures for blanks in your book.
| Principle | Rate | Compounded | Time | Amount | Interest |
| Rs. 5000 | 4% | Annually | 10 years | ? | ? |
| ? | 4% | Quarterly | 5 years | 17615.20 | ? |
Q- 4. The PTCL charges its subscribers Rs. 174 as line rent per month plus Rs. 2 per unit used. If the cost of using telephone is a function of the number of units used. Answer the following questions.
a. Copy the following table in your answer sheet and fill in the amount of telephone bill a consumer using the number of units in the top row will have to pay.
| Number of units | 0 | 50 | 100 | 150 | 200 |
| Telephone Bill Amount | | | | | |
b. Write the algebraic expression for this function which shows the cost C(n) for each number “n” of units used.
Q- 5. Use the discriminate to determine the nature of solution of the following equations:
2
a. 3 X + 16 X = 4X + 12
2
b. – 2X + X = 5
Q- 6. Find the points at which maximum or minimum values occur for the following functions:
2
a. Y = X – X – 6
2
b. Y = X + 5X + 6
Q-7. Let A = 1 -2 B = -1 2
2 0 1 1
2 2
Verify that A – B is not equal to (A + B) (A – B)
Q- 8. Find the determinate of the following matrix & explain whether it is a singular or non singular matrix:
4 3
8 15
Q- 9. If 6 of the 28 students in a class did not enroll in the college merit scholarship plan, what percentage did not enroll in the plan?
Q-10.Redraw the following table in your answer book and put the place value and Binary value in the table in your answer book for a Binary number 101101. 1101
| Place value | | | | | | | | | |
| Binary value | | | | | | | | | |
Section –C
(Marks: 16)
Q-11. a. ABC Corporation had a profit of Rs. 600,000 in 1981. In 1982 profit were 50% more than in 1981. Profits in 1983 were down 35% from the level of profits in 1982. Compute the profits for each year.
B . In two years from now some machinery in your company will need replacing. It is estimated that Rs. 500,000/- will be required for new machinery. To provide for this, Rs. X is to be allocated now invested at 12% compounded quarterly. What is the amount “X”.
Q-12. a. Five identical machines produce the same parts at the same rate. The five machines complete the required number of parts in 1.8 hours. How many hours does it take 3 machines to produce the same number of parts.
b. the cost and selling price of merchandise are listed in the table below. Determine the cost to selling price ratio and the cost to profit ratio.
| Items | cost | Selling price | Ratio of cost to Selling price | Ratio of cost to profit |
| A | Rs. 60 | Rs.96 | ? | ? |
| B | Rs.105 | RS.180 | ? | ? |
| C | RS.18 | Rs.33 | ? | ? |
| D | RS.204 | Rs.440 | ? | ? |
Q-13 a. A price of lumber 12 feet long is cut into two unequal lengths .
One piece is three times as long as the other.
i. Find the length of the shorter piece.
ii. Find length of the longer piece.
b. Mrs. B. invested Rs. 30,000 part at 5% and part at 8% . The total interest on the investment was
Rs. 2,100. How much did she invest at each rate?
3 1
C. If A = 4 3 B = 4 -1 C = 2
5 6 2 3 3
i. Describe the dimensions of the given matrices.
ii. Which of the following products are possible?
AB AC BC CA
iii. Compute the matrices for the products you decided were possible.
RATIO: A ratio is a relationship between two or more quantities stated in the same units of measurement. The ratios are used in business to find out the relative importance of figures. A ratio may be expressed by division ( / ) or by putting colon ( : ) between two numbers. The first number is called the Antecedent and the second number is Consequent.
PROPORTION: A proportion is the equality of two or more ratios. It can be stated as A: B: : C: D. It is read A is proportion to B and C is to D. The end terms of the proportion are called extremes. The middle terms of the proportion are called means. In proportion the product of the means is equal to the product of the extremes.
"A proportion may be stated in number of ways, the fractional
form of the equality of two ratios being preferable"
TYPES OF PROPORTION:
(a).Inverse Proportion: When two quantities are related to each other and the first becomes greater and second becomes smaller Or second becomes greater and first becomes smaller, it is known as a inverse proportion. Examples i. The more men working, less the time is taken to do a job.
ii. The greater the speed , less time is taken to cover a distance.
(b).Direct Proportion: When two quantities are related to each other and the first becomes greater when the second also becomes greater Or second becomes smaller when the first becomes, it is known as a direct proportion .Examples: i. The decrease number of units, decreases the total price.
ii. Increase the distance, increase the time to cover the distance.
(c).Compound Proportion: In certain problem we have to deal simultaneously with more than one proportion. The mutual relationship of proportions in such situations is known as compound proportion.
(d).Continued Proportions: Quantities are said to be in continued proportion when the first is related to the second, second is related to the third and the third is related to the fourth & so on.
PERCENTAGE: The word Percent stems from the Latin word Per Centum (by the hundred). With The passage of time the phrase was reduced to Per Cent but now it is stated as a single word Percent. Percent means hundredths. It is symbolized by the use of sign %. Percentage is the product of the base and rate. The base is the quantity regarded as a unit or as a whole. The rate is the number of hundredths of the base used. Percentage of a number = Base Χ Rate %.
MARK UP: The difference in the cost of the goods and the selling price is called Mark up or Profit. The Percentage of Mark up may be based on either the cost or the selling price.
Mark up = Sale Price – Cost Price.
Formula for cost, when % age profit is given: Cost = Sale Price
1+ % Profit
Formula for cost, when %age of loss given: Cost =
I -- % Loss
DISCOUNT: Discount is a deduction from the price of goods by the seller to the purchaser.
Discount = Price x Rate
100
Total Price = Discount x 100
Rate of Discount
(i) CASH DISCOUNT : It is a deduction or allowance given by a creditor to a debtor if the amount due is paid by the debtor before the due date.
(ii) TRADE DISCOUNT : Discount allowed by manufacturer or wholesaler at the time of selling
goods to retailer as a deduction from the listed price or catalogue price, is called Trade Discount.
COMMISSION: The amount of remuneration is called the commission, which is paid to a person who give his services. The Person who gives his services for others is called an agent. The commission is based on the value of goods bought or sold and is generally on percentage basis.
Commission = Total Price X Rate
100
INTEREST: If you borrow money, you also pay rent for its use, in the form of a fractional part of the money borrowed. This rental charge for borrowed money is known as Interest.
“INTEREST IS MONEY PAID FOR THE USE OF MONEY”
(i) SIMPLE INTEREST : Interest paid on the principle borrowed is called simple interest.
To calculate the simple interest we use the formula.
Simple Interest =Principal x Rate % x time OR I = P x R x T.
Where P = Principle sum or amount borrowed, R = The Rate of Interest, T = Time for which the principle is borrowed.
(ii) COMPUND INTEREST : Where the interest for each period is added to the principal before interest is calculated for the next period. The sum of the original interest is called the compound amount and the difference between the compound amount and the original principal is compound interest.
A = P (1 + r/100) n
ANNUITY: An annuity is a fixed amount of money that is paid or received at regular intervals or a set of equal payments made at equal intervals of time such as annually, semi annually, quarterly or monthly is called an annuity.
Payment Interval: The time between Successive payments of an annuity is its payments interval.
Term: The time from the beginning of the first interval to the end of the last interval is called its term. Annuity can be classified into two categories.
An annunity may be classified in any of the following three classes:
i. Ordinary Annunity. ii. Annunity Due. iii. Perpetuity.
i. Ordinary Annunity: An annunity is considered as to be ordinary annunity if each payment is made at the end of each payment period and continue for a definite period.
ii. Annunity Due: An annunity is considered as to be annunity de if each payment is made at the beginning of each payment period and continue for a definite period.
iii. Perpetuity: An annuity is considered as to be perpetuity if the payments starts on a certain date and continue for indefinite period.
Annunity Certain: An annunity certain is one in which the payments begin and end on fixed dates.
Contingent Annunity: In a contingent annunity the payments are related to events that can not be placed regularly. Annunites which have an infinite duration in which beginning or termination is dependent in some uncertain event are known as contingent annunites.
Amount or Sum of an annunity: The sum of all payment plus all interest earned is called the amount of the annunity or future value of the annunity.
Characteristics of Annunity:
i. The amount of payment is usually identical throughout the term of annunity.
ii. The interval of time in each payment period of an annunity usually constant such as annually, half annually , quarterly or monthly.
iii. Growth rate of money remains constant throughout the term of annunity and charged compounded.
Application of Annunity in Business:
Several modern business as given below depends on the concept of an annunity.
i. Business of insurance companies, Business of leasing companies.
ii. Business of goods sold on installments, Business of house building finance corporation.
iii. Business of bound or Debentures.
RESENT VALUE OF AN ANNUITY: The term annuity is used to describe on account into which a person makes equal periodic payments (deposits). This term is also used to describe an account from which a person receives equal periodic payments, (withdrawals), that is, if you invest lump sum of money in an account today, so that at regular intervals you will receive a fixed sum of money. This lump sum is called the present value of annuity. Sum of Ordinary Annuity and Annunity Due:
Following formulas are used to calculate sum of ordinary and annunity due.
i. For Ordinary Annunity : S = R ( 1 + i ) - 1 , For Annunity Due: S = R ( 1 + i ) - 1 - R
i i
Amortization: There are many ways of borrowing money or retiring a debt. One of these methods is called the amortization. An interest bearing debt is defined amortized if both principle and interest are paid by a sequence of equal payments made at equal periods of time. It is a method of payment in which borrowings with current interest are repaid in equal periodic installments.
MATRICES:
The mathematical study of matrix began with the work of the English mathematicians, Arthur Cayley (1821-1895) and James Sylvester (1814-1897).
Definition: A matrix is a table of numbers or variables enclosed by a pair of brackets under the certain rules. Each number in a matrix is called an element or entry matrix. OR
A matrix is a rectangular array of elements.
Rows and Column of Matrix: In a matrix, the horizontal lines are called rows of matrix and the vertical lines are called column of matrix.
Order Of Matrix/ Dimension: The number of rows and columns in a matrix is called the order of the matrix. If a matrix A has m rows and n columns, it is said to be of order m by n which is written as m x n. 1 2 3
3 5 6
Here number of rows = m = 2 and number of column = n= 3. So order of the matrix = m x n = 2 x 3
TYPES OF MATRIX:
(1).Square Matrix: If the number of rows and number of columns of a matrix are equal, the matrix is called a Square matrix. 2 3
3 5
(2).Zero Or Null Matrix: A zero or null matrix is a matrix in which every element is zero.
0 0 0
0 0 0
(3).Identity Matrix: It is square matrix and all elements on its main diagonal are one i.e. where as all other elements are zero. 1 0 0
0 0 1
1 0 0
The function of identity matrix is similar to the function of unity inshade ordinary arithmetic.
(4).Diagonal Matrix: It is a matrix which all elements are zero except the main diagonal which consist of numbers other than one. 3 0 0
0 0 7
5 0 0
(5).Inverse Of Matrix: The inverse of a number a is 1/a relationship also exists between a matrix and inverse of the matrix in all square matrices.
(6)Equality of Two Matrices: Two matrices are equal subject to fulfillment of two conditions.
a).Their dimension or order is the same.
b).Their corresponding elements are also equal to each other.
1 3 1 3
2 5 2 5
(7).Transpose Of Matrix: If the rows and columns of a matrix are interchanged the resulting matrix is called the transpose of the given matrix.
3 2
3 2 4 2 3
2 3 7 4 7
Row Matrix: A matrix having single row but several columns is called row matrix. A = [ 1 2 3 ]
Column Matrix: A matrix having single column but several rows is called a column matrix.
Notation: Matrices are usually denoted by the capital letters A, B, C ………Z.
Elements of matrices are denoted by small letters and are called scalars. The elements of the matrices are usually enclosed within square brackets [ ] or parentheses, ( ). Matrices are also conveniently denoted by writing a typical entry within brackets and by specifying the order of the matrix.
ARITHEMATIC OPERATION OF MATRICES:
(1).Addition: If two matrices have the same order, they are said to be confirmable for addition. Two matrices can be added only if they have the same dimension. The resulting matrix will also have the same dimension be adding their respective elements.
(2).Subtraction: The corresponding elements of two matrices of the same dimension or order may be subtracted in the same manner as we do in addition. The resulting matrix will also have the same dimension after subtracting.
(3).Multiplication Of Matrix: Before attempting to multiply two matrices, it is essential to check that the number of columns of first matrix is equal to the number of rows of the second matrix. If it is so, the two matrices are compatible for m multiplication otherwise not.
The elements of the first row of A are multiplied by the corresponding elements of first column B. The product is summed and is placed in the first row first column element of the resultant matrix. Similarly, the elements of the second row of matrix A are multiplied by corresponding elements of the first column B, the product is summed and is placed in the second row first column element of the resultant matrix. The process is repeated for other elements.
Determinant of a Matrix: A determinant is a square arrangement of numbers in rows and columns enclosed in two vertical line segments. we read A as the determinant of A and net as the absolute value of A. If
2 5 3 5
1 2 1 2
= (3 x 2) – ( 5 x 5 ) = 6 – 5 = 1
Singular Matrix: A square matrix is A is said to be singular, if value of its corresponding determinant is zero. [ A ] = 0
Non Singular Matrix: A square matrix A is said to be non singular, if value of its corresponding determinant is not zero. A = 0
Adjoint Matrix: Adjoint Matrix is defined as the transpose matrix of cofactors matrix of given matrix. if A is a square matrix and A is its matrix of cofactors then Adjoint matrix of A is denoted by Adj (A) and defined by: Adj ( A) = ( A )
INVERSE OF A MATRIX: The method of finding the inverse of a matrix can be simplified by using the determinant. If A is a square matrix, the A-1 will be the inverse of A such that
AA-1 = 1
NOTE: The inverse of a singular matrix does not exist.
Method: To find the inverse of a square matrix, use the followings.
a). Interchange elements of the principle diagonal.
b).Change the signs of the elements of the other diagonal.
c).Divide the resulting matrix by [A].
BINARY NUMBER SYSTEM
Decimal Number System:
We do our ordinary counting and computation work in a system with base 10. This system is called Decimal System ( Decema = 10) .Numbers in base ten are expressed in terms of power 10. The first ten numbers can be expressed by a single digit. 0,1,2,3,4,5,6,7,8,9
The next number after 9 requires two digits to express it 10 Here 10 means not any ones and I ten the next number is 11 this means 1 one and 1 ten. etc.
Binary Number System: Computers are designed to operate internally in a binary number system(base two)It is a numerical system based on units of two. The only number symbols in base two are 0 and 1. The first number can be written with a single digit. 1 The next number after 1 requires two digits. 10 Here 10 means not any ones and 1 two.
| Decimal Number ( base 10) | Binary Number ( base 2) |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
BINARY CONVERSION OF DECIMAL NUMBER TO NUMBER
There are two methods to change the decimal numbers to the binary number.
Method-1 The first method of converting a number from base ten to base two is to divide
successively by 2 , recording the remainder. The method is explained with the help of following example.
Change 19 to base 2 2 19
2 9--------1
2 4--------1
2 2--------0
1-------0
To get the required binary number, start from the last remainder and proceeding upward; we get (19) = (10011)
Method-2The second method of converting a number from base ten to base two is to subtract the highest multiple of 2 which is less than the numbers and doing the same process with the remainder obtained after each step until the remainder is zero. The method is explained by the following example,
Convert the 93 to the binary numbers.
In order to include all powers of two from zero to six, this would be written as;
93= 1x2+0x2+1x2+1x2+1x2+0x2+1x2 = (1011101)
CONVERSION OF BINARY NUMBER TO DECIMAL NUMBER: The process of converting a binary number to a decimal number is actually a simple one. A binary number can be converted to a decimal number by adding the place values of individual digits of the binary number. In other words we can make a table of the powers of two and total only those powers which correspond to a 1 in the binary number. Convert the binary number 101101 in to the decimal number.
Thus (101101) = (1x32)+(0x16)+(1x8)+(1x4)+(0x2)+(1x1)
= 32+0+8+4+0+1
= (45)
Addition in Binary Number System: The operation of addition in binary system is carried out just in same way as in decimal system. The only difference is that in binary system we use only two integers i.e. 0 and 1 to express a number. Here we are presenting a table which will be helpful to you in addition of two numbers expressed in Binary Number System.
| Operation “ + “ | 0 | 1 |
| 0 | 0 | 1 |
| 1 | 1 | 10 |
0 + 0 = 0
0 + 1 = 1 + 0 = 1
1 + 1 = 10
Example: Add 10111 and 10011
10111
+ 10011
101010
Starting from the right, we add 1 and 1 get 2 is equivalent to 10 ( read one zero) in the binary system. we write 0 and carry 1 to add it to 1 + 1 i.e. 1 + 1 +1, the result is 11 ( read one , one). Writing 1 as the sum and carrying 1 ot add it to 1 + o , we get 1+0+1 which give 10 so that , we write 0 and carry 1 and so on.
Subtraction in Binary Number System: Subtraction is done as the inverse of addition. Recalling that subtraction is the inverse operation of addition leads to the following subtraction rules.
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
10- 1 = 1
Example: Subtract 1011 from 10000 1 1 1 10 -----------Borrowing
1 0 0 0 0 ----------- Minuend
1 0 1 1 -----------Subtrahend
0 1 0 1 ------------Difference
Multiplication in Binary Number System: The procedure of multiplication in binary Number System is same as in decimal system. 0 x 0 = 0 , 0 x 1 = 0 , 1 x 0 = 0 , 1 x 1 = 1
Binary Multiplication Table
| x | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 0 | 1 |
Example: Multiply the binary numbers 1011 and 101
1 0 1 1
x 1 0 1
1 0 1 1
0 0 0 0
1 0 1 1
1 1 0 1 1 1
Division in binary Number system: Division in binary number system is carried out by finding how many times the divisor can be subtracted from the dividend. This division can be done by repeated subtraction. Example: Divide 1010111 and 1110
1 0 1 0 1 1 1
1 1 1 0 First subtraction = 1
1 0 0 1 0 0 1 Remainder
1 1 1 0 Second subtraction = 1 + 1 = 10
1 0 1 1 0 1 Remainder
1 1 1 0 Third Substraction = 10 + 1 + 11
1 1 1 1 1 Remainder
1 1 1 0 Fourth subtraction = 11 + 1 = 100
1 0 0 0 1 Remainder
1 1 1 0 fifth subtraction 100 + 1 = 101
0 0 1 1 Remainder
Quotient = 101
Remainder = 11
Functions and their Graphs:
Functions : A function is a special type of input output relation that expresses how one quantity depends on another quantity. A function is a rule that assigns to each input value exactly one output value.
Domain: The set of all input values to which the rule applies is called the domain of the function or the set whose elements may serve as replacement for a variable is called the domain or the replacement set of the variable.
Open Sentences: Sentences containing variables are called open sentences.
Solution of An open Sentence: Elements of the replacement set ( domain) for which the open sentence is true are called the solutions of the open sentence over the domain.
Solution Set: The set of all solutions of an open sentence is called a solution set.
Cartesian Co-ordinates: We construct the co-ordinate system by drawing two real number lines perpendicular to each other so that they insect at their origins.
Origin: The point of intersection is called the origin of the system.
Co-ordinate axes: the two lines are called the co-ordinate axes. we call the horizontal axis the x-axis, and the vertical axis the y-axis. The axes divide the plane into four quadrants. To every point in the plane we assign an order pair of number. The first element in the pair is called the x-coordinate, and the second element of the pair is called the y-coordinate.
Graphical Representation of Functions:
Range: The set of all output values is called the range.
Variable: A variable is a quantity which during a discussion may take on any value of a set of values. The price of dozen of eggs, the weight of a person, the speed of an automobile, etc.
Constants: Quantities which do not change in value but which maintain a fixed value are called constants. The number of inches in a foot, the number of player in football team, the number of days in a week, etc.
Independent Variables in a Function: A variable that represents input variable for a function is called and independent variable.
Dependent Variable: A variable that represents output variable is called dependent variable because its values depends on the values of the independent variable.
Explicit Function : If y = f(x) is a function such that the dependent variable y is explicitly expressed in terms of an independent variable x, then the function f is called an explicit function.
Implicit Function: If f(x,y) = 0 is a function such that neither x nor y is emplicitly given one in terms of the other , than the function f is called an implicit function.
Replacement Sets: The set whose elements may serve as replacement for a variable is called the
Functional Relations: Equations and their Solutions:
Equation: An equation may be defined as a statement which clearly indicate that two algebraic expression are equal. The two expression are two sides of equation which are connected by the sing of equality.
Linear Equation: The equation in one or more variables with maximum power of each variable as one is called linear equation. The standard form of linear equation is single variable(x) is: ax + b = 0
Quadratic Equation: An equation in one or more variables with maximum power of variable ( s) as two is called quadratic equation. The standard form of quadratic equation in single variable x is given as under:
2
x+ bx + c = o
A quadratic equation is also called a second-degree equation or an equation of degree two. A quadratic equation usually have two different roots.
Solution set of a Quadratic Equation in Single Variable: A quadratic equation in one variable can be solved by taking one of the following method.
1. Method of Factorization. 2. Method of Completing Square. 3. Method of Quadratic Formula.
Quadratic Formula: The general quadratic equation can be solved by completing square. When this is done, a formula is obtained which can be used to solve any quadratic equation. This is called the quadratic formula. X = - b b - 4ac
2a
Simultaneous Equation: A set of equations (atleast two equations) developed in same problem involving same quantities (variables ) is called set of simultaneous equations.
Insert the correct option i.e. A/B/C/D in the empty box opposite each part. Each part carries one mark.
I A college has 80 teacher of which 60 are science teachers and 20 are humanities teachers. The ratio of 3 : 4 represents:
A. Humanities teachers to total number of teachers.
B. Science teachers to humanities teachers
C. Science teachers to total number of teachers
D. Humanities teachers to science teachers
ii. If Men Hours Rupees Days
50 20 8000 8
X 16 19200 20
Using the fundamental principle of proportion the number of men (X) in the above table is:
A. 10 B. 20 C. 30 D. 40
iii. A teacher’s salary in 2007 is 107.5% of her 2006 salary. If the 2006 salary was Rs 15000/- What is her 2007 salary?
A. Rs. 19150 B. 18120 C. 17140 D. Rs. 16125
iv. Mobeen earn a commission of 15% of gross sales. The level of sales he needs to earn Rs. 2340.
A. 16500 B. 15600 C. 14200 D. 13400
vi. Bank A offers 5.25 % compounded interest quarterly, bank B offers 5.5% interest compounded semi annually and bank C offers 5.75% interest compounded annually on their saving accounts. At which bank would you earn more interest?
A. Bank C B. Bank A C. Bank B. D. None of the above
vii. If the discriminant of the quadratic equations greater than zero then its roots would be:
A. Equal B. Rational C. Irrational D. Complex
viii. If there is no point of intersection and there is no pair of numbers that satisfies both of two equations, such equations are:
A. Dependent B. Consistent C. Independent D. Inconsistent
ix. Which of the given laws does not hold true for multiplication of matrices?
A. the commutative law B. The associative law C. The distributive law D. All laws.
x. While converting a binary fraction 101.1, the .1 is converted to :
0 -1 -2 -3
A. 2 B. 2 C. 2 D. 2
1. Net price is equal to:
A. List price + Trade discount + Cash discount. B. List price + Trade discount – Cash discount
C. List price – Trade discount – Cash discount D. List price - Trade discount + Cash discount
2. If price increases, quantity supply will also increase is the example of:
A. Continued proportion B. Direct proportion C. Indirect proportion D. Inverse proportion
3. If Men : Days
10 : X
By using the principles of proportion the number of days (X) in the above table is :
A . 30 days B. 20 days C. 45 days D. 35 days
4. If 20 men can prepare 10 office tables in a day . The number of men required to prepare 25 such office tables in a day are:
A. 25men B. 50 men C. 75men D. 100 men
5. If more men are working less time is required to do a job. This an example of:
A. Direct proportion B. Inverse proportion
C. Continuous proportion D. Compound Proportion
6. A profit of Rs. 458500 is earned from business by four partners. This profit is to be allocated to the four partners in the ratio 4/5: 1/8: 2/3: 4/7. The amount of profit to first partner is:
A. Rs.16 9,571.82 B. Rs. 26,495.59 C. Rs. 141,309.85 D. Rs. 121,111.73
7. A reduction in selling price or amount of bill that becomes the profit when article is sold at list price is called:
A. Trade discount B. Retail discount C. Cash discount D. Quantity discount
8. A broker received Rs. 16,000 for selling a price of land. His rate of commission was 2.5 %. The selling price is:
A. 540,000 B. 640000 C. 740000 D. 840000
9. The ratio between 11 Kg to 88 Kg is:
A. 1:8 B.
10. The ratio between 25 Kg to 625 Kg:
A. 1:25 B. 25:1 C. 1:5 D. 4:8
11. The ratio 4 to 8 is:
A. 2/1 B. ½ C. 2/2 D. 2/4
12. The ratio of 10 to 30 is equal to the ratio of:
A. 5 to 6 B. 1 to 3 C. 3 to 9 D. 2 to 3
13. The result obtained by addition is called:
A. Product B. Sum C. Difference D. Quotient
14. The result 3+3 x 3 is:
A. 27 B. 9 C. 12 D. 18
15. What will be the first order of operation?
A. (+ or - ) B. (+ or +) C. (+ or X) D. (x or %)
16. Khalid is as old as Akram and Akram is half as old as Hakam. The sum of ages is 120 years. The age of Khalid is : A. 50 years B. 25 years C. 30 years D. 20 years.
17. 30% of Rs. 1800 is: A. 450 B. 540 C. 240 D. 340
18. 0.045 when converted into percentage we get:
A. 4.5% B. 0.45 % C. 45% D. 045 %
19. 329 is what percentage of 5000? A. 329% B. 3.29 % C. 32.9% 
D. 6.58%
20. 80 is 25% of: A. 320 B. 360 C. 420 D. 520
21. Amount paid to an agent as remuneration of his services is called:
A. Brokerage B. Commission C. Salary D. Discount.
22. A price marked on the item on which retailer is agree to sale the item to general public is:
A. Market price B. Face value C. Book Price D. All of above
23. If 11 : 3 :: x : 9 , then the value of x will be: A. 9 B. 27 C. 33 D. 13
24. In
number of pupils is: A. 2:5 B. 3: 5 C. 4 : 6 D. 2:3
25. If 20 men can do a Job in 10 days, how many men will be required to do that job in 20 days?
A. 10 B. 20 C. 30 D. 15
26. A man earns Rs 1500 in 2 weeks. What he will earn in 2 days while he works 6 days in a week.
A. 250 B. 200 C. 150 D. 300
27. A person digs a tunnel of 5 KM in 10 days. In how many days he will dig a 15 KM long tunnel. A. 20 days B. 25 days C. 80 days D. 35 days
28. 10 men do a work in 4 days. In how many days 20 men will do the same work.
A. 4 days B. 2 days C. 6 days D. 8 days
29. Price of a shirt is Rs. 300 . The shopkeeper sold it a t a discount of 15% what is the amount of discount. A. 50 B. 40 C. 45 D. 60
30. Javed gave 1/40 of her wealth as Zakat. What percentage of his wealth has he given as zakat:
A. 3.5% B. 1.5 % C. 2.5 % D. 2%
31. 100% 1 and 1% of are both:
A. Equal B. 100% of 1 is greater C. 100% of 1 is lesser D. Not equal
32. Nadeem Purchased furniture for Rs. 8000 and sold it for Rs. 7000. Find the loss percent.
A. 12.5% B. 20% C. 11% D. 13.5 %
33. What number is 20 % more than Rs. 9000.
A. 11000 B. 10500 C. 10800 D. 10600
34. Percentage is actually ratio of any number with a standard number of:
A. 100 B. 50 C. 110 D. 200
35. Proportion may be initially of two types direct and second is:
A. Inverse B. Compound C Continuous D. Collective
36. The length of
Find the length of white part is:
A. 4 meter B. 6 meter C. 2 meter D. 3.5 meter
37. A milkman mixes milk with water in a ratio o f 8:4. If weight of pure milk is 60Kg. Than what is the weight including water:
A. 60 Kg. B. 90 Kg C. 20 Kg D . 55 kg
38. If 16.25 is converted into decimal, the decimal number is:
A. 1.625 B. 16.25 C. 0.1625 D. 162.5
39. A house wife spend ¾ of her money in the market and ½ of the remainder in the shop the fraction of her money left is:
A. 1/7 B. 2 / 7 C. 5/7 D. 3 /14
40. Asghar has Rs. P, Akbar Rs. D more than Asghar. Together they have:
A. Rs.(2P-D) B. Rs. (P- D) C. Rs. (P+D) D. Rs. (2P + D)
41. 0.17 as a percentage is:
A. 83% B. 17% C. 1.7 % D. 8.3 %
42. Rs.510 decreased by 2% is:
A. Rs. 510 B. Rs. 495 C. Rs. 498 D. Rs. 490
43. In
number of boys to the number of pupils is:
A. 2 : 5 B. 3 : 5 C. 4 : 6 D. 2 : 3
44. Waqas Zafar buys U.S $ 1000. The buying rate $ = Rs. 56.1235.
What is the total amount payable in Pak. rupees to the customer?
A. 56532.5 B. 65123.5 C. 55123.5 D. 56123.5
45. Ratio is the way of expressing relation ship between two:
A. Homogenous quantities B. Non-homogeneous quantities
C. Different quantities D. Inverse quantities
46. A ratio can be reduce to its:
A. Highest term B. Lowest term C Middle term D. None of the above
47. The investments of two persons in a business of a Rs. 80000 and Rs. 20000.
Hence, Second invested:
A. Half of first B. 4th times than C. ¼th of the first D. ½ of the first
48. Direct and inverse proportions are two:
A. Basic types B. Final types C. Constant types D. Second types
49. Every percentage can be converted into:
A. Decimal fraction B. Ratio C. Proportion D. A and B
50. Commission on a deal is Rs. 6000 @ 3 %. What is the amount of the deal?
A. 60000 B. 100000 C. 150000 D. 200000
51. Cost price of an article would be, if sale price = Rs. 100 and loss = 20 %:
A. Rs. 125 B. Rs. 150 C. Rs. 600 D. Rs. 500
52. Given 20 : 5 :: 64 : X ? The missing term is:
A. 4 B. 16 C. 24 D. 32
53. Prt is used to calculate:
A. Annuity B. Simple interest C. Compound interest D. None of these
54. Money borrowed remains fixed in:
A . Annuity B. Compound Interest C. Simple interest D. Both A and B
55. The sum borrowed is called:
A. Interest B. Amount C. Principal D. None of above
56. In Islam, Interest is:
A. Forbidden B. allowed C. Partially forbidden D. Partially allowed
57. Amount is calculated by:
A. Principal + Interest B. Principal – Interest C. Principal x Interest D. None
58. The time between successive receipts or payments of an annuity is kno2wn as >
A. Receipt interval B. Payment interval C. Receipt period D. Payment period
59. When the term of an annuity is fixed or defined is called:
A. Annuity due B. Ordinary annuity C. Contingent annuity D. Annuity certain
60. If the payment are made at the end of each payment interval, it is called:
A. Annuity due B. Ordinary annuity C. simple annuity D. None of above
61. If the payments are made at the beginning of each payment interval is called:
A . annuity due B. Ordinary annuity C. Contingent annuity D. None of above
62. If the payments or receipts are made on a certain date and continue for indefinite period of time, is called:
A. Ordinary annuity B. Perpetuity annuity C. Annuity due D. annuity certain
63. the exhausts of some of an annuity is called:
A. Present value B. Perpetuity C. Face value D. Both a & B.
64. What will be the simple interest on Rs. 500 borrowed for 4 years at 11% per annum?
A. 120 B. 220 C. 320 D. 250
65. Rs/. 700 invested at 4% per annum. How long it will take for to reach the amount Rs. 784?
A. 2 years B. 4 years C. one year D. 3 years
66. Annuity is used in:
A. Economics B. mathematics of Finance C. Algebra D. both b and c.
67. An equation is a statement that two expressions are:
A. not equal to zero b. Zero C. equal D. Neon of above
2
68. What from of graph of this equation y= X -2X - 5
A. Parabola B. Parallel line C. Straight line D. None of above.
69. Common solution of simultaneous system of equation can also be obtained by:
A. Use of matrix algebra B. Use of Graphs C. Both a & d D. None of above
70. Liner equation has:
A. No root B. Two roots C. one root D. none of above
71. Linear equation is solve through the formula of:
A. Factorization B. Quadratic formula C. both a & C. D. Transposition
72. A quadratic equation is also known as:
A. Polynomial equation B. Third degree equation C. Second Degree equation d. None
73. The equation with the highest power of one is called:
A. Linear equation B. cubic equation C. quadratic equation D. None of above
74. An equation with highest power of two is called:
A. Linear equation B. Quadratic equation C. Homogenous equation D. Rational equation.
75. Simultaneous equations can be solved by:
A. Elimination by substitution method B. Factorization method
C. Eliminating by addition or Subsection D. Both a & c.
76. What symbol that can be replaced by any one of a set of different numbers.
A. constant B. Data C. Variable D. equation.
77. If a matrix has m rows and n columns then its order is:
A . m + n B. m x m C. mx n D. n x n
78. The order of the matrix [ 2 5 7 ] is:
A. 1 x 3 B. 1 x 1 C. 3x 1 D. 3 x 3
79. A matrix having m rows and n columns with m = n is called:
A. Zero matrix B. Square matrix C. Rectangular matrix D. Scaloar matrix
80. If A is a matrix of order m x n and B is matrix of order n x p then order of AB is:
A. n x p B. b. p x m C. p x n D. m x p
81. [ 0 0 0] is:
A. Null matrix B . Scalar matrix C. Identity matrix D. diagonal matrix
82. The transpose of a row matrix is a :
A. Column matrix B. diagonal matrix C. Diagonal matrix D. Scalar matrix
83. A matix having equal number of rows and columns is called:
A. Equal matix B. Scalar matrix C. diagonal matrix
84. A quantity which adopts different values during a discussion is called:
A. Parameter B. Constant C. Variable D. none of above
85. A quantity which does not change is called:
A . Parameter B. constant C. Variable D. None of above
86. The domain and range consists of numbers is called:
A. Graphs B . Real number C. values D. Real values
Fill in the blanks:
1. The ______ term of ratio is called antecedent.( first)
2. The ______ term of ratio is called consequent.( second)
3. The ratio does not change if multiplied by ______ number.( same)
4. The ratio does not change to divided by _____ number.(same)
5. A ratio is a ______ between two more quantities.(relationship)
6. The number appearing in ratios are called ______.(terms)
7. Materials are mixed in given ______ to make products.(ratios)
8. Partnership profits are distributed in agreed ____. (ratio)
9. The sum of _____ of ratios is total amount for allocation.(terms)
10. The duplicate ratio of 4 is ____. ( )
11. The sub-duplicate ratio of 25 is ____.( 25)
12. The inverse ratio of 4: 5 is _____ .(5:4)
13. Relation between two homogeneous quantities or numbers can be expressed by a ______.( ratio)
14. 5/4 to 1/8 is the same as _____.(10 to 1)
15. ______ is the equality of two ratios.(Proportion)
16. 5 : 3 : : 20 : 12 is read as_______ ( 5 is to 3 as 20 is to 12)
17. The first and fourth terms of a proportion are _____.( Extremes)
18. The second and third terms of a proportion are called _____.( Means)
19 Product of two extremes = ______.(Product of two means)
20 Product of means when divided by any one of extremes given the other ____(Extreme)
21. 4 : 3 : : ? : 27 ______.( 36)
22. Proportions may be direct or ______ ( Inversely)
23. If both the quantities involved in a proportion move in same direction then they are said to be ______. proportional.( Direct)
24. If both the quantities involved in a proportion move in opposite direction then they are said to be ______ proportional.( inversely)
25. The price of 15 note books is 300 then price of 80 note books will be ___( 1600)
26. A fraction with denominator 100 is called _____.(Percentage)
27. 56% - 8% = _____( 7%)
28. Decimal form of 3.5% is ______.(0.035)
29. 25% of 500 is ______.(125)
30. 50 is _____ % of 450.(11.11%)
31. 680 is 80% of ________.(850)
32. Cash discount is charged on the amount after the deduction of ______ discount.(Trade)
33. Invoice price = List price - _____.(Trade discount)
34. Net price = _____ - _____ - ____ ( List price – Trade discount – cash discount)
35. The percentage involved in commission is called ____.(Rate of commission)
36. 8 ¼ % OF _____ IS 206.25(2500)
37. Profit = ________ - ______ (Selling price – Cost Price)
38. Loss = ________ - _______( Cost price – Selling Price)
39. Selling price = ______ + _____(Cost price + Profit)
:40. Cost = Selling price ( Profit percentage)
1 + ______
41. 24.64 reduced to its lowest form is ______.( 3:8)
42. _______ is defined as the ratio of any number with a standard 100.(percentage)
43. Discount means reduction in _____.(selling price)
44. Selling price is also called _____.(Face price)
45. Cost = _____.( 1 + Profit %)
46. To compute percentage gain or loss we use______( gain or loss x 100)
Cost price
47. A proportion has ____ terms.(four)
48. A proportion is _____ of two or more ratios.(equality)
49. Direct proportion is suitable for calculating____ cost.( variable)
50. Inverse proportion is used to find out ____cost.(fixed)
51. Percent is a fraction whose denominator is _____ ( 100)
52. Percentage is equal to rate multiplied by _____.(base)
53. Base is the entire or whole amount which means hindered.(%)
54. Percentage is the fractional portion of the _____.(base)
55. Rate is the figure with ______ sing after it.(%)
56. When the rate is ___than 100% the percentage is larger than the base.(more)
57. The _____ is a fractional part of the base.(rate)
58. The percentage formula is ____.(Rate x Base)
59. The formula for finding the rate is ____ ( P/B)
60. The mark up is a profit percent base on _____.(Cost)
61. The margin is a profit percent base on ______.(sales)
62. The mark up can be converted into _____ and vice versa.(margin)
63. The formula for calculating the base is _____.(Price x 100/Rate)
Interest and Annunities
1. Interest is classified into two classes which are ____ and ______.( simple interest, compound interest)
2. In ______ interest the capital remains fixed.( Simple interest)
3. The amount of money paid for the use of money is called ______.( interest)
4. Amount = _____ + _____(Principal , Interest)
5. The money invested or borrowed of which interest is paid is called ______.(Principal)
6. The percentage return is called______.(Rate percent)
7. Simple interest = ____x____x____.(Principal x Rate x Time)
n
8. P[ 1 + r) – 1 ] = ________.(Compound interest)
9. In _____ interest, the interest due at the end of each year is added to the principal for the next year.( compound interest)
10. An ______ is a series of payments, usually equal , make at equal intervals of time.( Annunity)
11. The interval between successive payment of an annunity is called______.( Payment period)
12. If the payments are made at the end of payment period of an annunity is ____.( ordinary)
13. The time interval in each payment period of an annunity is ______.( Fixed)
14. Growth rate of money remains constant during the whole term of annunity and charged ______.( compounded)
15. Present value of annunity is ______ sum of annunity.( The largest )
16. To calculate ordinary annunity we use the formula S = _________. n
( R [ 1 + i) – 1 ] - R )
i
17. To calculate annunity due we use the formula S = _____ (n+i)
( R [ 1 + i ) - 1 ] - R
i
18. When the payment interval and interest conversion period are same, the annunity is called_____.( simple annunity)
19. Accumulated value = Payment x ________.(Accumulation Factor)
20. When the payments are made at the end of each payment intervals the annunity is called _______.( ordinary)
21. In ________ the term of annunity is fixed.( Annunity certain)
22. In ______ the term of annunity depends upon uncertain events.( contingent annunity)
23. In _______ annunity the payment interval and interest conversion are not same .( General)
24. The ______ has a payment at the beginning of each interest period but one at the end of term.( annunity due)
25. In the formula I indicates _______.( Interest rate per period of an annunity)
26. In ______ interest every term period interest included in the capital to calculate interest of next period interest.( compound)
27. _________ is the amount of money invested or borrowed on which interest is to be made.( Principal )
28 ___ of money remains constant throughout the terms of annuity and charged compounded.( growth rate)
29. An annunity is considered to be ______ if the payment starts on a certain date and continue for indefinite period.( Perpetuity)
30. The idea of _____ of an annunity is just reverse of sum of an annunity. ( present value)
31. The payment is made at the start of the period under ____ due. ( annunity)
33. The payment is made some time after the end of first period under _____( deferred )
34. When payments begin on certain date and continue indefinitely is called _____ annunity.( perpetuity)
35. When term of annunity depends upon some uncertain even it is called ______ annunity.( contingent)
36. It is _______ annunity earns interest for two or more periods after last payment.( simple)
37. A ____ annunity earns interest for two or more periods after last payment.( forborne)
38. A sequence of equal payments made at equal period of time is called ______ .( annunity)
39. When payments begin and end at fixed time it is called annunity______.( Certain)
40. The time between successive payments of an annuntiy is called payment_____.( interval)
41. The time between first payment and last payment is called ____ of annunity.( term)
42. It is ______ annunity when payment interval and interest conversion period differs. (general)
43. The value of all payments at the end of the term is called _____ value.( accumulated)
44. The value of all payments at the start of the term is called ____value.( discounted)
45. Net present value is a _____ of discounted cash flow.( technique)
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