1. Express 87 % as a fraction. 87 1 2 17 = = 2 7 8 2. Express the fraction as a percentage. 1 2 = = 12 1 % 8 2 2 3. Express 200 as a percentage of 00. 200 = 40% 00 4. In a school there are 300 boys and 200 girls. Find the percentage of total number of girls as a percentage of total number of boys in the school. 200 200 2 = = 66 % 300 3 3. Two numbers are respectively 20% and 2% of a third number, what percentage is the first of the second? 3 rd = 1 st = 20 2 nd = 2 20 = 2 6. Two numbers are respectively 30% and 40% less than a third number. What percent is the second of the first? 3 rd = 1 st = 70% 2 nd = 60% 60 600 = = 8 % 70 7 7 7. Monthly income of Seeta is 20% more than Rita. Monthly income of Rita is 2% less than that of Geeta. If the difference between the monthly income of Seeta and Geeta is Rs.300, find the difference between the monthly income of Rita and Geeta. S:R = 120: = 6: R:G = 7: = 3:4 Hence S:R:G = 18:1:20 Rs.300 We have = Rs. 70 2 Compiled By: Anjan Page 1
8. A is 20% more than B and B is 2% more than C. find A:C. A:B = 120: = 6: B:C = 12: = :4 Hence A:B:C = 30:2:20 = 6::4 Therefore A:C = 6:4 = 3:2 9. A is 2% less than that of B whereas C is 40% more than B. Find A:B:C. A:B = 7: = 3:4 B:C = :140 = :7 Hence A:B:C = 1:20:28 10. The income of C is 20% more than that of B. the income of B is 2% more than that of A. By what percent is the income of C is more than that of A? C : B = 120 : = 6 : B : A = 12 : = C : B : A = : 4 30 : 2 : 20 = 6 : : 4 6 4 Re q. Percent = = 0% 4 11. A positive number is divided by instead of being multiplied by. What percent is the result of the required correct value? N = 4% N 12. The salary of Ram decreases from Rs.700 to Rs.630. Find the percentage decrease in his salary. 630 700 = 10% = 10% Decrease 700 13. The salary of Ram increases from Rs.630 to Rs.700. Find the percentage increase in his salary. 700 630 = 11 1 % 630 9 14. A positive number is by mistake multiplied by instead of being divided by. By what percent more or less than the correct answer is the result obtained? N N 2 1 = = 2400% More N 1 1. The difference between 20% and 39% of a number is 38. What is the 2% of that number? 38 2% = 0 19% 16. The difference between 20% and 39% of a number is 38. Find the number. 38 % = 200 19% 17. If Rs.200 is increased by 10%, find the final amount. 110 Rs.200 Rs. 200 = Rs.220 OR 110% = Rs.220 % Compiled By: Anjan Page 2
18. An amount is increased by 1% and becomes Rs.230. What was the amount? Rs.230 Rs. 230 = Rs.200 11 OR 110% = Rs.200 11% 19. If Rs.20 id decreased by 20%, find the final amount. 80 Rs.20 Rs. 20 = Rs.200 OR = Rs.200 % 20. An amount is decreased by 10% and becomes Rs.360. what was the amount? Rs.360 Rs. 360 = Rs.400 90 OR % = Rs.400 90% 21. When numerator of a fraction is increased by 10% and denominator decreased by 20%, the resultant fraction becomes /8. Find the original fraction. % 110% 80 = = 8 8 110 11 % 22. If the numerator of a fraction is increased by 200% and the denominator is increased by 400% the resultant fraction becomes 7/, find the original fraction. 7 % 300% 7 00 7 = = 300 3 % 00% 23. The ratio of the monthly income of A, B and C is 2:4: respectively. If the monthly income of A, B and C is increased by 20%, 2% and 0% respectively, find the new ratio of their monthly income. 2 % 120% : 4 % 12% : % 10% = 240 : 00 : 70 = 24 : 0 : 7 24. Ram spends 20% of his monthly salary on house rent, 10% on food, 1% on travel, 10% on clothes and the remaining amount of Rs.2200 is saved. What is the monthly salary of Ram? Rs.2200 % = Rs.0000 4% 2. A man spends 40% of his monthly salary on food, 20% on house rent, 12% on travel and 10% on education. After all these expenditures he saved Rs.7200. find 1) The amount spent on travel. 2) The amount spent on education. 3) Find his monthly salary. Rs.7200 1) 12% = Rs. 4800 18% Rs.7200 2) 10% = Rs. 4000 18% Compiled By: Anjan Page 3
Rs.7200 3) % = Rs. 40000 18% 26. In a factory 60% workers are more than 30 years and 7% among them are males and remaining are females. If the number of male workers more than 30 years is 130, what is the total number of workers in the factory? 130 % = 3000 7 60% 27. Amit spends 40% of the amount he received from his father on hostel expenses, 20% on books and stationary and 0% of the remaining on transport. After the above expenses he is left with Rs.900. how much money did he get from his father? Rs. 900 = Rs.400 0 40 28. A man loses 12.% of his money and, after spending 70% of the remainder, he is left with Rs.210. how much had he at first? Rs. 210 = Rs.800 30 87. 29. After deducting 10% from a certain sum, and then 20% from the remainder, there is Rs.3600 left. Find the original sum. Rs. 3600 = Rs.000 80 90 30. A man had Rs.4800 in his locker two years ago. In the first year, he deposited 20% of the amount in his locker. In the second year, he deposited 2% of the increased amount in his locker. Find the amount at present in his locker. 120 12 Rs. 4800 = Rs.7200 31. In a library 20% of the books are in Hindi, 0% of the remaining are in English and 30% of the remaining are in French. The remaining 6300 books are in regional language. What is the total number of books in the library? 6300 = 22000 70 0 80 32. If the annual increase in the population of a town is 4% and the present number of people is 162, what will the population be in 3 years? 104 104 104 162 = 1776 33. If the annual increase in the population of a town is 4% and the present population is 1776, what was it three years ago? 1776 = 162 104 104 104 Compiled By: Anjan Page 4
34. The population of a town is 8000. It increases by 10% during the first year and by 20% during the second year. What is the population after two years? 110 120 8000 = 1060 3. The population of a town is 00. It increases by 10% during the first year. During the second year, it decreases by 20% and increased by 30% during the third year. What is the population after 3 years? 110 80 130 00 = 11440 36. During one year, the population of a locality increases by % but during the next year, it decreases by %. If the population at the end of the second year was 7980, find the population at the beginning of the first year. 7980 = 8000 9 10 37. The population of a town increases at the rate of 10% during one year and it decreases at the rate of 10% during the second year. If it has 29700 people at present, find the number of people two years ago. 29700 = 30000 90 110 38. If A s salary is 2% more than that of B, then how much percent is B s salary less than that of A? 2 % = 20% 12 39. If A s salary is 30% less than that of B, then how much percent is B s salary more than that of A? 6 30 % = 42 % 70 7 40. If the price of sugar raised by 20%, find by how much percent must a householder reduce its consumption so as not to increase expenditure in this item? 2 20 % = 16 % 120 3 41. If the price of sugar falls by 10%, find by how much percent must a householder increase its consumption so as not to decrease expenditure in this item? 1 10 % = 11 % 90 9 42. The price of a commodity rises from Rs.6/kg to Rs.7./kg. if the expenditure cannot increase, find the percentage of reduction in the consumption of that commodity so that the expenditure cannot increase. 7. 6 % age Increase in Pr ice = = 2% 6 Re quired Percentage = 2% = 20% 12 Compiled By: Anjan Page
43. In an examination, a candidate must get marks to pass. If a candidate, who gets 210 marks, fails by 0 marks, find the maximum marks. ( 210 + 0) 260 % = % = 32 44. A student has to secure 40% marks to pass. If he gets 40 marks and fails by 40 marks, find the maximum marks set for the examination. ( 40 + 40) 80 % = % = 200 40% 40% 4. In an examination it is required to get 290 of the aggregate marks to pass. A student gets 209 marks and is failed by 12% marks. What are the maximum aggregate marks a student can get? ( 290 209) 81 % = % = 67 12% 12% 46. A candidate who gets 30% of the marks in a test fails by 0 marks. Another candidate who gets 320 marks fails by 30 marks. Find the maximum marks. [( 320 + 30) 0] 300 % = % = 0 30% 30% 47. A candidate scores 2% and fails by 30 marks, while another candidate who scores 0% marks, gets 20 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination. [ 20 ( 30) ] 0 % = % = 200 0% 2% 2% [ ] 48. In an exam, A scores 280 marks which are 20 more than passing marks. B got marks which are 60 more than the passing marks. What is the passing percentage of the exam? ( 280 20) = 260 = 6% 280 20 + 60 320 [( ) ] 49. A student got a total of 70% marks in an exam of 4 subjects. In the three subjects he scores 81, 66 and 60 marks. If the maximum marks of each subject are, then find the marks obtained in 4 th subject. 4 70% ( 81+ 66 + 60) = 73 % 0. A solution of salt and water contains 1% salt by weight. Of it 30 kg water evaporates and the solution now contains 20% of salt. Find the original quantity of salt. S W 1% : 8% 3:17 3:17 20% : 1:4 3:12 30 kg 3 = 18 kg Compiled By: Anjan Page 6
1. 40 liters mixture of milk and water contain 10% of water. How much water must be added to make the water 20% in the new mixture? M W 90% : 10% 9:1 36:4 : 20% 4:1 36:9 40 liters = liters 40 2. What quantity of water should be added to reduce 9 liters of 0% acidic liquid to 30% acidic liquid? A W 0% : 0% 1:1 3:3 30% : 70% 3:7 3:7 9 liters 4 = 6 liters 6 3. In 2 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%? I S 20% : 1:4 10% : 90% 1:9 2 kg = 2 kg 4. The salary of a worker is first increased by 10% and thereafter it was reduced by 10%. What was the change in his salary? 10 10 10 10 = 1% = 1% Decrease. A shopkeeper marks the price of his goods 12% higher than its original price. After that he allows a discount of 12%. What is his percentage profit or loss? 12 12 12 12 = 1.44% = 1% loss 6. If the population of a town is increased by 1% in the first year and is decreased by 1% in the next year, what effect can be seen in the population of that town? 1 1 1 1 = 2.2% = 2.2% Decrease 7. The salary of a worker was first increased by 10% and thereafter decreased by %. What was the change in his salary? 10 10 = 4.% Increase 8. A shopkeeper marks the price of his goods 20% higher than its original price. After that he allows a discount of 10%. What is his percentage profit or loss? 20 10 20 10 = 8% Pr ofit Compiled By: Anjan Page 7
9. The population of a town was reduced by 12% in the year 1988. In 1989, it was increased by 1%. What is the percentage effect on the population in the beginning of 1990? 12 1 12 + 1 = 1.2% Increase 60. The tax on a commodity is diminished by 20% and its consumption increased by 1%. Find the effect on revenue. 20 1 20 + 1 = 8% = 8% Decrease 61. If the price is increased by 10% and sale is decreased by %, then what will be the effect on income? 10 10 = 4.% Increase 62. In measuring the sides of a rectangle, one side is taken % in excess and the other 4% in deficit. Find the error percent in area calculated from the measurement. 4 4 = 0.8% Increase 63. If one side of a rectangle is increased by 20% and the other is increased by %, find the percent value by which the area changes. 20 20 + + = 26% Increase 64. If the sides of a square are increased by 30%, find the percent increase in its area. 30 30 30 + 30 + = 69% Increase 6. If the sides of a rectangle are increased by 10%, what is the percentage increase in its area? 10 10 10 + 10 + = 21% Increase 66. If the radius of a circle is decreased by %, find the error percentage in area calculated from the measurement. + = 9.7% = 9.7 Decrease Compiled By: Anjan Page 8