PERCENTAGE AND ITS APPLICATION

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1 9 PERCENTAGE AND ITS APPLICATION.(A) Express each of the following statements in the percentage form : (i) eggs out of 30 are good (ii) 47 students out of 50 are present (iii) Rs 34 out of Rs 00 is spent. Ans. (i) eggs out of 30 are good = % 30 = = (ii) 47 students out of 50 are present = % 50 = = (iii) Rs 34 out of Rs 00 is spent = = = 67% (B) Express the following fractions as percents : (i) Ans. (i) = = = 8 % or 8.5% Ans. (i) 08% = = =.08 (ii) 50 (ii) (ii) % 5 = = (C) Express as percents : (i) 0.09 (ii) 0.03 (iii) (iv) 0.90 Ans. (i) = = 9% (ii) 88 (iii) = = 8.8% (iv) 0 (D) Convert into fractions in lowest terms : (i) Ans. (i) % (ii) 6 % 3 (iii) 5 5 % = % = = = = 3.% = = 90% 37 % (iv) (ii) 6 % % = % = = (iii) 37 % = % = = (iv) 6 % = % = = (E) Express as decimal fractions: (i) 08% (ii) 9.% % = = =

2 . (i) What percent of 95 is 9? 9 Ans. Required percentage = = = 0% 95 5 (ii) What percent of 65 is 7? Ans. Required percentage = % 65 = = (iii) What percent of 4 is 9.4? 94 Ans. Required percentage = % 0 4 = = 3. (i) What percent is 6 P of Re? Ans. Required percentage = (ii) What is 6 mm of cm? Ans. Required percentage = 6mm cm = (iii) What percent is 8 cm of m? 6 p 6 = = 6% ( Re = p) Re p 6mm 60% 0 mm = Ans. Required percentage = 8cm m = 8cm 8% m = ( m = cm) 4. (i) What percent is 89 m of.05 km? Ans. Required percentage = 89m.05km = m (ii) What percent is 75 gm of.5 kg? Ans. Required percentage = 75gm.5kg 75gm =.5 gm = 7% (iii) What percent is minute 4 seconds of hour? = 890 8% 05 = Ans. Required percentage = minute4seconds hour = ( )seconds 60 60seconds (iv) What per cent is 3 4 litre of 4 litres? = 44 4% = Ans. Required percentage = 3 litre 4 = 4 litres = 50 % = 6 % 3 3

3 5. What is the number whose 8% is 8? Ans. Let the number be x. As per condition, 8 8% of x = 8 8 x = 8 x = = 9 5 = 5 8 Thus, the number is What is the number whose 6% is 8.? Ans. Let the number be x 6% of x = x = 8. x = 6 Thus, the number is 35, 7. What is the amount whose % is Rs? Ans. Let the amount be x. As per condition, % of x = Rs x = x = = 7 5 = 75. Thus, the amount = Rs What is the length whose 6% is 36 cm? Ans. Let the length be x, As per condition, 6 6% of x = 36 cm 36 x = 36 x = = 9 5 = 5 6 Thus, the length = 5 cm = 5 m =.5 m 9. What is the number whose.5% is 3.5? Ans. Let the number be x. As per condition,.5% of x = x = = = = x = = = 7 4 = Thus, the number is A class contains 5 children, out of which 6 are girls. What percentage of the class are boys? Ans. Total number of students = 5. Number of boys = (5 6) = 9 Thus, percentage of boys = 9 5 = 76% 3

4 . A girls gets 65 marks out of 80. What percent of marks did she get? Ans. Total marks = 80. Marks obtained by the girl = 65 Required percentage = = % 4 =. In a class test, the marks were awarded out of 80. Kamal obtained 65% marks. How many marks did he get? Ans. Total marks = 80. Kamal obtained = 65% of 80 = 80 = = In an examination, Renu obtained 480 marks out of 750. What percentage of marks did she get? Ans. Total marks = 750. Renu obtained marks = Thus, percentage of marks she get = 0 = = 64% In her annual examination Geeta scored 39 marks out of 60 in English and 5 out of 75 in Hindi. In which subject her performance was better? Ans. Percentage of marks in English = = 39 5 = 65% Thus, percentage of marks in Hindi = = = 68% 75 3 In Hindi Geeta s performance is better. 5. In an examination, 640 students appeared. Of them, 544 passed and the rest failed. What percentage of students failed? Ans. Total sutdents = 640, Passed students = 544, Failed students = = 96 Percentage of failed students = = 6 % = 5% In a plot of ground of area 6000 sq. mm only 4500sq. m is allowed for construction. What percent is to be left without construction? Ans. Total area of the ground = 6000 sq. m. Area allowed for construction = 4500 sq. m. Area left without construction = 6,000 sq. m 4500 sq. m = 500 sq.m Thus, percentage of the ground without construction = 500 5% 6000 = 7. The population of a small locality was 4000 in 979 and became 4500 in 98. By what percent did the population increase? Ans. Production in year 979 = Production in year 98 =

5 Increase in population = ( ) = 500 Thus, percentage of increase in population = 500.5% 4000 = 8. The price of a scooter was Rs 8000 in 975. It reduced to Rs 6000 in 980. By what percent did the price of the scooter reduce? Ans. Original cost of scooter = Rs 8000 Reduced cost of scooter = Rs 6000 Reduction in price of scooter = Rs 8,000 Rs 6,000 = Rs,000 Thus, percentage of reduction = = 5% 9. In an examination 360 students appeared. Of them, 85% passed. How many students failed? Ans. Total students = 360. Number of students passed = 85% of 360 = = Thus, failed students = = A tin contained 5 litres of oil. Due to leaksage litres of oil was lost. What percentage of oil is still there in the tin? Ans. Total oil in the tin = 5 litres oil leak out = litres. Oil left in the tin = (5 ) litres = 3 litres. Thus, percentage of oil left in tin = % 5 = =. An alloy consists of copper and zinc. It contains 64% copper and rest is zinc. Find the quantity of copper and zinc in 45 g of this alloy? Ans. Total alloy = 45 gm. Quantity of copper in alloy = 64% of 45 gm = gm = 64 7 = 7gm 4 Thus, quantity of zinc in alloy = (45 7) gm = 53 gm.. Mr Mehat had Rs Out of this money, he gave 0% to his daughter, 35% to his son. 30% to his wife and the rest he donated to a Charitable trust. How much did he donate to the Charitable trust? Ans. Total money = Rs Daughter s share = 0% of Rs 5600 = Rs = Rs 50. Son s share = 35% of Rs 5600 = Rs = Rs

6 Wife s share = 30% of Rs 5600 = Rs = Rs 7680 Amount he donated to a Charitable Trust = Rs [5600 ( )] = Rs [ ] = Rs Mr. Vasudevan was a clerk in bank. His salary was Rs 850 per month. Now, he has been promoted as an accountant. His salary is now Rs Find the percentage increase in his salary. Ans. Total salary = Rs 850 per month. After promontion total salary = Rs 9735 per month. Increase in salary = Rs ( ) = Rs Thus, percentage of increased in salary = = 0 = 8% A tank holds 6 litres of water. At present, it is 35% full. How many litres of water must be put into it so that it is 60% full? Ans. Let total capacity of tank = x litres At present water in tank = 35% of x litres = 35 6 x = x = = litres = 360 litres 35 7 Thus, total capacity of tank = 360 litres 60% of water in tank = 60% of 360 = litres = 6 litres Hence required water to be put into tank = (6 6) litres = 90 litres 5. On a particular day, 96% students were present in a school. If the number of obsentees on that day was 54, find the total strength of school. Ans. Student present in school = 96%. Present age of absentees percentage = ( 96)% = 4%. Let total strength of school be x, then = 4% of x = x = 54 x = x = 54 5 = Thus strength of school = In an examination, a student has to secure 48% marks to pass. If Rahul gets 47 marks and fails by 5 marks, what are the maximum marks? Ans. Let the maximum mark be x. Passing marks = 48% of x = x 5 6

7 As per condition, x 47 5 x = + = x = = 5 = 55 Thus, maximum marks = 5 7. The value of a car depreciates (decreases) by 0% every year. If its present value is Rs 8,60, what will be its value after one year? Ans. Present value of car = Rs 8560 Depreciates every year = 0% of Rs 8560 = Rs = Rs 856. Value of car after one year = Rs ( ) = Rs The price of a radio was Rs 675. Now, its price has been increased by 6%. What is the increased price of the radio? 6 Ans. Price of radio = Rs 675. Increase in price = 6% of Rs 675 = Rs 675 = Rs = Rs = Rs Increased price of radio = Rs ( ) = Rs The price of a cooler during last summer was quoted at Rs 750. In off season, the price has been reduced by 4%. What is the reduced price of the cooler? Ans. Price of cooler = Rs 750 Reduction in price = 4% of Rs 750 = Rs = Rs 7 75 = Rs Reduced price of cooler = Rs ( ) = Rs An election was contested by two candidates A and B. In all there were voters. 80% of votes were polled. If A got 60% of total votes polled, how many votes did B get? Ans. Total voters = Votes polled = 80% of = = = Number of votes A got = 60% of = = = Number of votes B got = = Rate of basmati rice last year was Rs 40 a kg. This year they are costler by 0%. What is the price this year? 7

8 Ans. Rate of basmata rice = Rs 40 kg. Increase in rate = 0% 0 New price = = = Rs 48 per kg. 3. A tin contains 4 litres of milk. Due to leakage, 70 ml is lost. What percent of milk is still present in the tin? Ans. Total milk = 4 litre = 4 0 ml. = 4000 ml. Lost milk = 70 ml. Milk left in the tin = 4000 ml 70 ml = 380 ml Percentage of milk = = = 97% During October, a shop sold sarees worth Rs.40 lakhs. In the festival month of November, it sold sarees worth Rs.68 lakhs. Find the percentage increase in the sale. Ans. Sale in Oct. = Rs.40 lakh. Sale in Nov. = Rs.68 lakh. Increase in sale = 0.8 lakh Percentage of increase in sale = = 8 = = 0% A person having a monthly salary of Rs 3600 earns 5% raise.find his new monthly salary. Ans. Original salary = Rs Increased salary 5 = = = Rs In a student election, Rahul got 66% of the votes polled. If he got 363 votes, find the total number of votes polled. Ans. Let the total votes be x. Number of votes Rahul got = % of x = x = 363 = = 550 votes The population of a village has decreased by 6%. If the original population was 3650, find the population after decrease. Ans. Original population = 3650 Percentage of decrease in population = 6% 6 = = = Rajesh scored 555 marks out of a total of 600 marks and Ajay scored 473 marks out of a total of 550 marks. Whose performance is better? Ans. Percentage of Rajesh s mark = % 600 = 8

9 Percentage of Ajay s marks = = = = 86% 550 Thus, Rajesh has better performance % of the students in a school are girls. If the number of boys is 48, find : (i) the total strength of the school. (ii) number of girls in the school. Ans. (i) Let total student be x-percentage of girls = 43% Percentage of boys = 43 = 57% Number of boys = 48 57% of x = 48 x = 48 = Number of girls = (600 48) = (i) After an increase of 0% ; a number becomes 540. Find the original number. (ii) After a decrease of 35% ; number becomes 50. Find the original number. Ans. (i) Let the number be = x. 0% increase = 0 0x x = 0x As per condtion, x + = 540 x + 0 x = x = 540 x = = 90 5 = Thus, original number = 450 (ii) Let the number be x. 35% decrease As per condition, 35 35x = x = 35x x = 50 x 35 x = x = 65x = 50 x = = 0 40 = Thus, original number = A boy got 60 out of 80 in Hindi, 75 out of 90 in English and 35 out of 40 in Arithmetic. In which subject his percentage of marks is best? Ans. In Hindi marks precentage of his obtained by the boy = = 75% Percentage of marks obtained by boy in English = = = 83.33% 9

10 Percentage of marks obtained by boy in Arithmetic = = 87 = 87.5% On comparing all percentage of marks in different subjects The boy scored highest marks in Arithmetics. 4. An agent gets commission at the rate of % on the business done by him. In a particular week, he does a business of Rs 50,000, find his commmission. 5 Ans. Total business done by agent = Rs 50,000. Rate of commission = % = % 5 Commission of agrent = Rs 50,000 = 50 5 = Rs Out of a salary of Rs 4,500, I keep /3 as savings. Out of the remaining money, I spend 50% on food and 0% on house rent. How much do I spend on food and house rent? Ans. Total salary = Rs 4,500. Saving = 3 of 4,500 = Rs,500 Balance salary = Rs 4,500 Rs,500 = Rs 3,000 Amount spending on food = 50% of Rs 3,000 = 50 Rs 3,000 = Rs,500 Amount spend on house rent = 0% of Rs 3,000 = 0 Rs 3,000 = Rs 600 Thus, total amount spend on food and house rent = Rs (, ) = Rs, % of length of a flagpole is painted green, 45% is painted yellow and the remaining red. If the length of the pole is 8 m, what length of it is painted red? Ans. Total length of pole = 8 m. Green part = 0%. Yellow part = 45%. Red part =? 0 Length of pole painted green painted = 8 = 8 3.6m 5 = 45 9 Length of pole painted yellow = 8 = 8 = 8.m 0 Hence, length of pole painted red = 8 ( ) = 8.7 = 6.3 m. 44. A grocer bought 50 eggs at 5 for Rs 8 and sold them at for Rs 5. Find : (i) the cost price of one egg ; (ii) the profit or loss on selling one egg ; (iii) his total profits or loss on selling all the eggs. Ans. (i) The cost price of one egg = Rs 8 5 = Rs.60 0

11 (ii) The cost price of one egg = Rs.60 The selling price of one egg = Rs.50 The profit on selling one egg = Rs = Rs 0.90 (iii) The cost price of 50 eggs = Rs = Rs 400 The selling price of 50 eggs = Rs = 65 Profit = Rs = Rs A cloth seller purchased 80 metres of cloth for Rs 340 and sold it at the rate of Rs 44 per metre. Find his profit or loss. Ans. The cost price of 80 metres = Rs 340. The selling price of 80 metres = Rs = Rs 350. Profit = Rs = Rs A fruit seller bougth 300 oranges at 6 for Rs 5 and sold them at 5 for Rs 6. Find : (i) the cost price of all the oranges; (ii) the selling price of all the oranges; (iii) his overall profit and profit percentage. Ans. (i) The cost price of one orange = Rs 5 6. The cost price of 300 orange = Rs = Rs 50 6 (ii) The selling price of one orange = Rs 6 5 The selling price of all the orange = Rs = Rs 360 (iii) CP of 300 orange = Rs 50. SP of 300 orange = Rs 360 Profit = S. P C. P = Rs = Rs 0 Profit percentage = 0 44% 50 = 47. A dealer buys a washing machine for Rs 500 and sells it for Rs Find his profit and profit percentage. Ans. Cost price of machine = Rs,500. Selling price of machine = Rs 3,500 Profit = S. P. C. P. = (3,500,500) = Rs 0 Profit % = Profit C.P 0 =,500 = 8% 48. A dealer buys a motor cycle for Rs and sells it for Rs Find his loss and loss percentage. Ans. Cost price of motor cycle = Rs 35,500; Selling price of motor cycle = Rs 33,370 Loss = C. P. S. P. = 35,500 33,370 = Rs 30 loss 30 Loss % = = = 6% C.P 35500

12 49. Mr Basu purchased 0 plastic chairs at Rs 5 per chair. He sold chairs at Rs 75 per chair and the remaining chairs at Rs 00 per chair. Find his gain or loss percent. Ans. Cost price of chair = Rs 5; Cost of 0 chair = 5 0 = Rs S. P. of chairs at the rate of Rs 75 per chair = 75 = Rs 3300 S. P. of 8 chairs at the rate of Rs 00 per chair = 8 00 = Rs 600 Total S. P. of 0 chairs = Rs Rs 600 = Rs 4900 Profit = S. P. C. P. = = Rs 400 Profit% = Profit = = = 8 % C.P A shopkeeper buys three articles for Rs 375, Rs 580, and Rs 48. He is able to sell these articles for Rs 436, Rs 635 and Rs 350 respectively. Find the gain or loss to the shopkeeper on the whole. Ans. C. P. of three articles = Rs Rs Rs 48 = Rs 83 S. P of three articles = Rs Rs Rs 350 = Rs 4 As S. P. is more than C. P. hence profit = S P C P = Rs 4 Rs 383 = Rs Rajesh buys an old sofa-set for Rs,50 and spends Rs 350 on its repairs. (i) Find the total cost price of the sofa to Rajesh. (ii) Find the profit or the loss made, if Rajesh is able to sell the repaired sofa-set for Rs,540. Ans. (i) Total C. P. of sofa-set = cost price of sofa + money spend on repairs = Rs,50 + Rs 350 = Rs 600 (ii) S. P. = Rs,540. Since S. P. is less than C. P. Loss = C. P. S. P. = Rs 600 Rs 540 = Rs A florish bought 40 roses at Rs 9 per dozen. If he sold all of them at Re each, what profit did he make? What is his profit percent? Ans. C. P. of rose = 9 = Rs S.P. of rose = Rs.00 Since S. P is more than C.P, hence Profit = S. P. C. P..00 Rs 0.75 = Rs 0.5 Profit on sale of rose = Rs 0.5 Profit on sale of 40 rose = 40 Rs 0.5 = Rs Profit% = Ppofit 0.5 C.P. = 0.75 = = 33 % At rate of Rs 0 per dozen, dozen eggs are bought. Two dozen eggs were broken. They were sold at Rs 5 per dozen. What was the gain or loss percent?

13 Ans. C. P. of one dozen of eggs = Rs 0 C.P. of dozen of eggs = Rs 0 = Rs 0 S.P. of one dozen of eggs = Rs 5 S. P. of 0 dozen ( dozen dozen broken) = Rs 5 0 = Rs 50 Profit = S. P. C. P = Rs 50 Rs 0 = Rs 30 Profit % = Profit = 30 5% C.P. 0 =. 54. A man purchased an iron safe for Rs 530 and paid Rs 80 on its transportation. He sold it for Rs 538. Find his loss per cent. Ans. C. P. of an iron safe = Rs 530. Amount spend on transportation = Rs 80 Net C. P. of iron safe = Rs ( ) = Rs 5400 S. P. of iron safe = Rs 538. Loss = Rs ( ) = Rs 6 Loss percentage = 6 3% 5400 = 55. A man bought a car for Rs He paid % of cost price to the broker and spent Rs 3400 on the repair of car. Then, he sold it for Rs Find gain percent. Ans. C. P. of car Rs Amount paid to broker = % of Rs = = Rs 600 Amount spent on repair = Rs Net C. P. of car = Rs ( ) = Rs S. P. of car = Rs Gain = Rs ( ) = Rs 6800 Gain% = % = 56. A grocer buys 08 eggs at Rs 5 per dozen and sells them at Rs.50 each. Find his gain per cent. Ans. The cost price of one egg = Rs 5 The cost price of 08 eggs = Rs 5 08 = Rs 5 9 = Rs 5 The selling price of 08 eggs = Rs = Rs 70 Gain = Rs 70 5 = Rs 45 Gain per cent = = = 0% A shopkeeper bought 50 kg of one variety of wheat at the rate of Rs 4.30 per kg and 5 kg of another variety at the rate of Rs 9.80 kg. He mixed the two varieties and sold the mixture at Rs 4.40 per kg. Find the profit per cent earned by the trader. 3

14 Ans. The cost price of one variety of wheat of 50 kg = Rs = Rs 75 The cost price of another vadriety of wheat of 5 kg = Rs = Rs 45 Total cost of mixture of wheat = Rs ( ) = Rs 960 The selling price of mixture of wheat = Rs = Rs 080 Profit = Rs ( ) = Rs 0 0 Profit precent = = = % A chair is sold for Rs 437 at a loss of 8%. At what price must it be sold to gain 8%? Ans. S.P. of the chair = Rs 437, Loss = 8% C.P. of the chair = Rs = Rs 437 = 437 = 5 9 =Rs Now, gain = 8%. S. P. of chair = Rs = Rs 475 = 7 9 = Rs A radio is sold for Rs 07 at a gain of 5% At what price must it be sold to gain 0%? Ans. S. P. of radio = Rs 07, Gain = 5% C. P. of radio = Rs Now, gain = 0% S. P of the radio = Rs = Rs 07 = 0 5 = Rs = Rs 0 00 = Rs 0 = Rs 60. A fan is sold for Rs 96 at a loss of 4%. At what price must it be sold it be sold to lose % only? Ans. S. P. fan = Rs 96, Loss = 4% C. P. of fan = Rs = Rs 96 = Rs Now, loss = % S. P. of fan = Rs 350 = Rs = = = Rs 33 4

15 6. A buys a transistor for Rs 45 and sells it to B at a gain of 6%. At what price did B buy it? If B sells it to C at a loss of 0%, what is the price paid by C? Ans. C.P. of transistor for A = Rs 45, gain = 6% + 6 Rs 6 S.P. of transistor by A = Rs 45 = 45 = Rs 493 C. P. of transistor for B = Rs 493, loss = 0% S. P. of transistor by B = Rs = Rs 493 = Rs 4437 = Rs C. P of transistor for C = Rs A dialer bought two table lamps for Rs 750 each. He sold one of the lamps at 0% gain and the other at 5% loss. Find his gain per cent on the whole transaction. Ans. The cost price of two table lamps = Rs 750 = Rs Selling price ot the one lamp = Rs = Rs = Rs 85 The selling price of the another lamp 5 = Rs = Rs ( ) = Rs 7.50 Total selling price = Rs ( ) = Rs Gain = Rs ( ) = Rs Gain per cent on the whole transaction = = = % A man borrowed Rs 500 from a bank at the rate of 9 % per annum simple interest. Find the amount that he has to pay at the end of 3 years, to clear off the debt. Ans. Hence P = Rs 500. R = y = Time = t = 3 years 9 9 % = % S. I = Rs = Rs = Rs = Rs Amount = P + S. I. = Rs ( ) = Rs To clear off the debt the man has to pay = Rs at the end of 3years, 64. A man borrowed Rs 4 lakhs from a bank at 8% per annum simple interest. At the end of years, he cleared his debt by paying Rs 4.5 lakhs and his old ear. Calculate the market value of the old car. 5

16 Ans. P = 4 lakh, R = 8%, Time = S.I = P R T Amount after years = 5 years = =,80,000 = (4,00,000 +,80,000) = Rs 5,80,000. Amount paid = Rs 4,5,000 Value of old car = Rs 5,80,000 Rs 4, 5,000 = Rs,55, Raghu borrowed Rs 0400 from a money lender at 8 % per annum simple interest. After a period of years 9 months, he gave Rs 853 and a buffalo to clear off the debt. What is the cost of the buffalo? 7 Ans. Here, P = Rs R = 8 % = % Time = years 9 month = 9 + years = years = 4 years S.I. = Rs = Rs 3 7 = Rs 43 4 Amount = P + S. I. = Rs ( ) = Rs 83 Cost of the buffalo = Rs (83 853) = Rs Find the principal that will yield an interest of Rs 306 in years at 9% per annum? Ans. Let Principal be Rs x. R = 9%, T = years S. I. = P R T x 9 = = Rs 9 x 9 x = 306 (given) x = = Rs = The principal = Rs On what sum of money the simple interest at 8% per annum would be Rs 936 in 9 months. Ans. Let principal be Rs x. R = 8%. T = 9 months = 9 years = 3 4 years 8 3 S. I. = P R T x = = Rs 3 x 3x = (given)

17 x = = Rs 3 50 = Thus, sum of money = Rs What sum will amount to Rs 508 at 7% per annum in 3years? Ans. Let principal be x. R = 7% = 3 years P R T x 7 3 S. I. = = = Rs x Amount = P + S. I. = x + x x + x 508 = 508 x = = 4 = 400 Thus, sum of money = Rs Rohan borrowed a certain sum from David at 7 % per annum simple interest. After a period of years 8 months, he paid Rs 304 to David and settled the accounts. What sum did he borrow? Ans. Let the sum be Rs. Then, P =. R = = 8 = % = % per annum, T = years 8 months = 8 P R T 5 8 S.I. = = Rs. = Rs 4 5 =Rs 0 3 Thus, Amount = Rs. ( + 0) = Rs 0 If the amount is Rs 0, then sum = Rs If the amount is Rs 304, then sum = Rs Thus, the sum borrowed was Rs = Rs 0 5 = Rs In how many years, the simple interest on Rs 5000 will be Rs 5 at annum? 5 Ans. P = Rs 5000, R = 7 = % S.I. = Rs % per

18 S.I. Time = = 5 75 = = 3 years. P R At what rate per cent per annum will Rs 640 amount to Rs 968 in Ans. Here, P = Rs 640, A = Rs 968, T = S. I = Rs ( ) = Rs 38 years 5 years years? Let the rate be R% per annum. R = S. I 38 = % = 8% P T Hence, the rate of interest is 8% per annum. 7. In how many years would a sum of money double itself at 8% per annum? Ans. Let sum of money (P) = Rs x, Amount = Rs x (given) Rate = 8% per annum, S.I = Rs ( x x) = Rs x S.I. x 5 T = = = Time = years. P R x At what rate percent per annum will a sum of money be five times of itself in 0 years? Ans. Let the principal be Rs. Amount = 5 time of principal = 5 = Rs 500 Interest = Rs 500 Rs = Rs 400. Time = 0 R = I 400 = = 40% P T 0 8

according to the (+)ve and the (-)ve signs respectively.

according to the (+)ve and the (-)ve signs respectively. Profit & Loss Cost Price: The price for which an article is purchased is called the Cost Price (C.P.) Selling price : The price at which an article is sold is called the Selling Price (S.P.) Profit (Gain)