PERCENTAGES

RECAP
Percentage Change, Change of Base, Successive Percentage Change:

1. If the length of a rectangle decreases by 40% and width increases by 30% then find the percentage
change in area of the rectangle.
(a) 32 % (b) - 22 % (c) 24 % (d) - 36 %
2. When the cost of petrol increases by 50% a man has to decrease his expenditure by 30%. Find the
percentage increase in the total expenditure.
(a) 4 (b) 5 (c) 2 (d) 1
3. Salary of A is 20% more than salary of B. By what percentage salary of B is less than salary of
A? (a) 12.5% (b) 16.66% (c) 25% (d) 33.33%
4. Percentage Increase in the price of sugar is 40%. A person wants his expenses to increase by
not more than 20%. By what minimum percentage should he decrease his consumption so that
his expenses are not exceeding by more than 20%?
(a) 14.28% (b) 12.5% (c) 28.56% (d) None of these
5. In a class, 65% of the students are boys. On a particular day 80% of girl students were present. What
was the fraction of boys present that day, if total no. of students present that day was 52%?
(a) 8/15 (b) 24/65 (c) 9/12 (d) 9/17
6. If Rs1000/- is increased by 40% then decreased by 20% and again increased by 30%, what is the new
amount (in Rs) that we get.
(a) 1456 (b) 1458 (c) 1487 (d) 1428
7. An electrical mechanic purchases a certain amount of wire, 10% of which was stolen. After using
85% of remainder he had 47m and 25cm left, how much did he purchase?
(a) 341 (b) 350 (c) 450 (d) 305
8. Price of tea is increased by 20% and due to this a man is able to purchase 4 kgs less, than what was
available earlier, for Rs. 120. What is the increased price of tea/kg?
(a) Rs. 4 (b) Rs. 5 (c) Rs.6 (d) Rs. 12
9. In an exam, it is required to get 36% of the total marks to pass. A student got 113 marks and failed by 85
marks. The maximum marks is -
(a) 800 (b) 550 (c) 600 (d) 400
10. In an exam it is required to get 40% marks to pass and a student got 72 mark and fails by 8 marks.
Find the total marks.
(a) 300 (b) 200 (c) 600 (d) 500
11. A sum of money increases by 20%, 30%, & 40% successively, then what is the overall %age increase in
the initial amount.
(a) 112 (b) 118.4 (c) 115 (d) 117
12. A fruit vendor threw away 20% of the fruits and sold 60% of the remaining. What percentage of fruits is
left with him?
(a) 32 (b) 25 (c) 30 (d) 18
13. 30% of the population in a class are females. If there are 490 males then the no. of females are
(a) 500 (b) 400 (c) 300 (d) 210
14. Shyam spent 20% of his pocket money on food and then 30% of the remainder on jeans. What
percentage of the original money is he left with?
(a) 64 (b) 44 (c) 56 (d) 36
15. Prem’s salary increase by 10% every year. What is the percentage increase in his salary after 3 years?
(a) 2.1 (b) 33.1 (c) 25 (d) 26
16. The manufacturer increases the price by 10% and then decreases by 20%, then what is the net percentage
decrease in price.
(a) 12% (b) 16% (c) 20% (d) 25%
17. The prices increased by 40% then by 20% and finally dropped by 15%. What is the overall percentage
change in prices?
(a) 34.8 (b) 42.8 (c) 32.5 (d) 49
18. In India there are 16 players out of these 50% are out of form and out of these 50% are Batsmen. How
many Indian batsmen are in form?
(a) 8 (b) 4 (c) 7 (d) 9
19. In IIM-B there are 60% Engineers out of these 30% are computer engineers, and 50% of these opt for
systems out of the rest 30% will take marketing. What percentage of the total batch who will take
marketing are computer engineers?
(a) 3.2 (b) 4.5 (c) 2.7 (d) 5.4
20. What is 20% of 40% of 60% of 80?
(a) 38.4 (b) 3.84 (c) 0.384 (d) None of these
Foundation Level
1. What percent of a day is 6 hours?
A) 25% B) 52% C) 50% D) 5%
2. Two-fifth of one-third of three seventh of a number is 15.What is 40% of that number?
A) 501 B) 105 C) 525 D) 150

3. The population of a town is 176000.If it increase at the rate of 5% per annum, what will be it’s population 2 years hence?
A) 194000 B)194040 C) 190440 D) 194104

4. The length and breath of a rectangle are increased by 20% and 30%.The area of the resulting rectangle exceeds the area of
the original rectangle?
A) 50% B) 65% C) 56% D) 156%

5. Water tax is increased by 20% but its consumption is decreased by 20%.Then increase or decrease in the expenditure of
the money is:
A) 40% B) 4% C) 96% D) None of the these.

6. Sugar contain 5% water .What quantity of pure Sugar should be added to 10 litres of sugar to reduce this to 2%.
A) 5 B) 6 C) 10 D) 15
7. In an election between 2 candidates, Candidate who gets 40% of the total vote defeated by 15000.The no of votes polled
by winner?
A) 10000 B) 45000 C) 30000 D) 6000
8. The price of a fan is decreased by 20%.as a result of which the sale increased by 40%.What will be the effect on the total
revenue of the shop?
A) 12% B) 10% C) 20% D) 30%
9. Raj save 10%,after 2 years when his income is increased by 10%,he could save the same money then how much his
expenditure increased?
A) 10% B) 20% C) 5% D) 15%
10. If x% of y is equal to z then what percentage of z is x?
A) y² /100 B) x²/100 C) 100²/y D) 100²/x

11. 45% of ? = 25% of 355

A) 195 B)176 C)127 D)197.22

12. MilK contain 10% of water. What quantity of pure milk is should be added to 15litre of milk to reduce the water
percentage is 7% ?
A)6 lit B)6.4 lit C)6.2 lit D)6.6 lit
13. Out of 500 students of a school 35% students plays football, 25% plays cricket and 20% neither play football nor cricket.
How many students play football and cricket?
A)200 B)100 C)50 D)94
14. The price of sugar is reduced by 3%.How many kg of sugar can now be bought for the money which was sufficient to buy
50kg of sugar earlier ?
A)50kg B)55kg C)51.5kg D)56kg

15. Fresh fruits contain 70% of water and dry fruits contain 20% of water. How much dry fruit can be obtained from 100kg of
fresh fruits?
A)35 B)37 C)37.5 D)40
16. In an examination , full mark is 500, A gets 25% more than B, B gets 40% more than C and C gets 60% more than D. If A
got 320 ,what percentage of full marks did D got (approx)?
A)21 B)22 C)23 D)24
17. If Harish height is 30% less than that of Yokesh , How much percentage Yokesh height is more than that of Harish ?
A)42.58% B)42.8% C)42.83% D)42.85%
18. Depreciation applicable to an equipment is 25.%. The value of the equipment after 4 years from now will be less by(in
percentage)?
A) 68.36% B)68.63% C)68.33% D)68.66%

19. The population of a city is increased 5% ,7% and 11% in the last three years, What will be the present population if the
population of a town was 2,40,000 three years ago ?
A)2,99,600 B)2,99,500 C)2,99,400 D)2,99,300
20. 500 pencils were distributed equally among children in such a way that the number of pencil received by each child is
20% of the total number of children. How many pencil did each child receive?
A)45 B)55 C)10 D)43
21. One type of liquid contains 20% water and the second type of liquid contains 35% water. A glass filled with 8 parts of the
first liquid and 5 parts of the second liquid. The water percentage in the new mixture is:
A)25.75 B)25.76 C)25.67
D)25.56 E)None of these
22. In an examination there are 3 subjects Maths, Science and Social of 100 marks each. Ganesh scores 60% and 80% in
Maths and Science. He scored 70% in aggregate. His Percentage of mark in Social is:
A)50 B)60 C)70
D)80 E)None of these
23. If the radius of the circle is increased by 5% then the area is increased by:
A)10.20 B)10.22 C)10.24
D)10.25 E)None of these

24. A number is mistakenly divided by 8 instead of being multiplied by 8.What is the percentage of error in the result?
A)98.43 B)98.34 C)95.76
D)97.76 E)None of these

25. A book consist of 45 pages, 30 lines on each page and 60 character on each line. If this content is written in another note
book consisting of 40 lines and 32 character per line then the required no of pages will be how much percentage more than
the previous no of pages ?
A)20% B)30% C)40%
D)50% E)None of these

26. In an election a candidate who got 25% of the total votes polled was defeated by his rival by 270 votes. Assuming that
there were only 2 candidates in the election, the total number of votes polled was :
A)400 B)500 C)440
D)540 E)None of these

27. The total number of girls in a class is 45% more than the total number of boys in the class. The total number of students in
the class is 294 then what is the difference between the total number of girls and boys ?
A)54 B)52 C)76 D)78 E)70
28. The population of a town is 16500.During the last 3 years, the population increased at the rate of 20% per year. The
population 3 years ago was:
A)9546 B)9547 C)9548 D)9549 E)9550

29. The mean annual salary paid to all employees was Rs.5000.The mean annual salary paid to all male and female workers
were Rs.5200 and Rs.4200.The percentage of female worker in the company is :
A)80% B)20% C)60% D)40% E)None of these

30. The passing marks in an examination is 40%.If Ashok gets 88 marks and is declared failed by 10 marks, then the
maximum mark in the examination is:
A)240 B)242 C)245 D)246 E)None of these

31. From the salary, Akhilesh spent 15% for house rent, 5% for children’s education and 15% for entertainment. Now he left
with Rs.13,000. His salary is:
A)19,000 B)20,000 C)18,000 D)15,000
32. In a School, 40% of the students are female and thus the no of boys exceed the no of girls by 40.Find the total no of
students.
A)190 B)100 C)200 D)180
33. In an examination 30% of the students failed in Science, 45% of the students failed in Maths and 25% of the students
failed in both subjects. Find the % of the students passed?
A)60% B)30% C)45% D)50%

34. In an examination Ammu scored 56% marks, Saran scored 90% marks and Rima scored 650 marks that is 65% then find
the total marks of three students ?
A)2110 B)1250 C)2450 D)2010
35. The salary of a workers increased by 15% and decreased by 7%, What % change rises in his salary ?
A)10% B)7% C)5% D)8%

36. The population of a village is decreased by 12% and 10% in 2 successive years. What % population is decreased after 2
years ?
A)18.4% B)30.6% C)20.8% D)23.5%
37. In an examination, 30% of the maximum marks required to pass. A student get 120marks and failed by 90marks. Find the
maximum marks
A)800 B)720 C)650 D)700
38. P’s income is 20% more than Q’s income. How much % Q’s income less than P’s income ?
A)18.54% B)16.67% C)17.76% D)15.75%
39. The price of rice is increased by 15%. The percentage of reduction that a family should effect in that use of rice, so as not
to increase the expenditure is :
A)13% B)10% C)15% D)17%
40. The value of commodity depreciated 20% annually. If the value of commodity 3yrs ago was Rs.10,500,Find it’s present
value ?
A)3678 B)5700 C)4567 D)5376

41. If x is 20% more than y, then by what percent y is smaller than x.

a) 50/3 % b) 40/3 % c) 46/3 % d) 47/3 %
42. In an alloy, there is 15% of brass, to get 90 kg of brass, how much alloy is needed ?
a) 400 kg b) 500 kg c) 600 kg d) 700
43. 25 litre of solution contains alcohol and water in the ratio 2:3. How much alcohol must be added to the solution to make a
solution containing 60% of alcohol ?
a) 10.5 ltr b) 11.5 lt c) 12.5 ltr d) 13.5 ltr
44. In an examination if a person get 20% of the marks then it is fail by 30 marks. Another person who gets 30% marks gets
30 marks more than the passing marks. Find out the total marks and the passing marks.
a) 600 and 150 b) 600 and 180
c) 500 and 150 d) 500 and 180
45. A company has produced 900 pieces of transistor out of which 15% are defective and out of remaining 20 % were not
sold. Find out the number of sold transistor.
a) 610 b) 611 c) 612 d) 614
46. In an election the votes between the winner and loser candidate are in the ratio 5:1. If total number of eligible voters are
1000, out of which 12% did not cast their vote and among the remaining vote 10% declared invalid. What is the number of
votes the winner candidate get ?
a) 620 b) 630 c) 640 d) 660
47. If the price of a commodity is increased by 30%, by how much % a consumer must reduce his consumption so to keep the
expenditure same ?
a) 100/13 b) 200/13 c) 300/13 d) 400/13
48. 1000 sweets need to be distributed equally among the school students in such a way that each student gets sweet equal to
10% of total students. Then the number of sweets, each student gets.
a) 10 b) 12 c) 14 d) 16
49. Rishi salary is first increased by 20% and then decreased by 25%. How much percent the salary increased/decreased ?
a) 5% b) 10% c) 15% d)20%
50. The income of a person is 10000 and its expenditure is 6000 and thus saves 4000rs. In the next year his income is
increased by 10% and its expenditure increased by 20%. Now his saving is what percent lower than the previous saving.
a) 5% B) 7.5% c) 10% d) 15%
51. 40% of the students like Mathematics, 50% like English and 10% like both Mathematics and English. What % of the
students like neither English nor Mathematics?
A) 25% B) 10% C) 20% D) 60% E) 80%
52. A watermelon weighing 20 kg contains 96% of water by weight. It is put in sun for some time and some water evaporates
so that now it contains only 95% of water by weight. The new weight of watermelon would be?
A) 17 kg B) 15 kg C) 18.5 kg
D) 16 kg E) 18 kg

53. If the price of wheat is reduced by 2%. How many kilograms of wheat a person can buy with the same money which was
earlier sufficient to buy 49 kg of wheat?
A) 58 kg B) 60 kg C) 52 kg
D) 55 kg E) 50 kg

54. Monthly salary of A is 30% more than B’s monthly salary and B’s monthly salary is 20% less than C’s. If the difference
between the monthly salaries of A and C is Rs 800, then find the annual salary of B.
A) Rs 14,500 B) Rs 16,800 C) Rs 15,000
D) Rs 16,000 E) None

55. Mixture 1 contains 20% of water and mixture 2 contains 35% of water. 10 parts from 1st mixture and 4 parts from 2nd
mixture is taken and put in a glass. What is the percentage of water in the new mixture of glass?
A) 17 (5/7) % B) 24 (2/7)% C) 28 (1/5)%
D) 24 (1/7)% E)18 (2/7)%
56. 3 years ago the population of a town was 1,60,000. In the three respective years the population increased by 3%, 2.5% and
5% respectively. What is the population of town after 3 years?
A) 1,77,366 B) 1,66,733 C) 1,76,736
D) 1,80,766 E) 1,69,766

57. There are 2500 students who appeared for an examination. Out of these, 35% students failed in 1 subject and 42% in other
subject and 15% of students failed in both the subjects. How many of the students failed in either of the 2 subjects but not
in both?
A) 1925 B) 1175 C) 1275
D) 1100 E) 1800
58. A bucket is filled with water such that the weight of bucket alone is 25% its weight when it is filled with water. Now
some of the water is removed from the bucket and now the weight of bucket along with remaining water is 50% of the
original total weight. What part of the water was removed from the bucket?
A) 2/5 B) ¼ C) 2/3 D) ½ E) 1/3
59. In a survey done by a committee, it was found that 4000 people have smoking habit. After a month this number rose by
5%. However due to continuous advices given by the committee to the people, the number reduced by 5% in the next
month and further by 10% in the next month. What is the total number of smokers after 3 months?
A) 3457 B) 3491 C) 3578
D) 3591 E) 3500

60. There are 5000 students in a school. The next year it was found that the number of boys and girls increased by 10% and
15% respectively making the total number of students in school as 5600. Find the number of girls originally in the school?
A) 4500 B) 2000 C) 3000
D) Cannot be determined E) none of these

61. If the price of an article is increased by 15%, then by how much the household should decrease their consumption so as to
keep his expenditure same.
A) 13(1/23)% B) 13(2/23)%
C) 11(1/23)% D) 11(2/23)%
E) None of these

62. The ratio between male and female in a city is 3: 7. The children percentage among the males and females of the city is 25
and 30 percent respectively. If the number of adult males in the city is 18000, then find the population of the town?
A) 70000 B) 80000 C) 85000
D) 95000 E) None of these
63. Pankaj gave 50 percent of the amount to Akash. Akash in turn gave two-fifth of the amount to Venu. After paying a bill of
500 rupees, Venu now have 8000 rupees left with him. Find the amount hold by Pankaj initially.
A) 41500 B) 42500 C) 43500
D) 44500 E) None of these
64. Rakesh spent 30 percent of his annual income on food items. Of the remaining amount he spent 60 percent on clothes and
bills. Now he save five-seventh of the remaining amount and the he saves 120000 yearly, then find his monthly income.
A) 40000 B) 50000 C) 60000
D) 70000 E)None of these
65. Weight of A and B are in the ratio of 3:5. If the weight of A is increased by 20 percent and then the total weight becomes
132 kg with an increase of 10 percent. B weight is increased by what percent.
A) 2% B) 3% C) 4%
D) 5% E)None of these

66. When the price of rice is increased by 25 percent, a family reduces its consumption such that the expenditure is only 10
percent more than before. If 40 kg of rice is consumed by family before, then find the new consumption of family.
A) 35.2 B) 35.2 C) 36.2
D) 37.2 E)None of these
67. The price of rice is increased by 20 percent and a person decrease his consumption by 15 percent, so his expenditure on
rice is-
A) increase by 2 percent B) increase by 4 percent C) decrease by 2 percent D) decrease by 4 percent
E)None of these
68. A salary is 40 percent more than B. B’s salary is 30 percent less than C. If the difference between the salary of C and A is
1200 rupees, then what is the monthly income of C?
A) 50000 B) 60000 C) 70000
D) 80000 E)None of these

69. When the price of rice is increased by 30 percent, a family reduces its consumption such that the expenditure is only 20
percent more than before. If 50 kg of rice is consumed by family before, then find the new consumption of family
(approx.) ?
A) 43kg B) 44kg C) 45kg D) 46kg E)None of these
70. One type of liquid contains 20 percent of milk and second type of liquid contains 40 percent milk. If 4 part of the first and
6 part of the second are mix, then what is the percent of water in the mixture.
A) 64% B) 66% C) 68%
D) 70% E)None of these

71. In a library 5 percent books are in English, 10 percent of the remaining are in Hindi and 15 percent of the remaining are in
Sanskrit. The remaining 11628 books are in French. Then find the total number of books in the library.
a) 8000 b) 12000 c) 16000
d) 20000 e) None of these

72. A solution contains 10% of salt by weight. On evaporation 15 litre of water evaporates and now concentration of salt
becomes 20 percent. Find the initial quantity of solution
a) 20ltr b) 30ltr c) 40ltr
d) 50ltr e) None of these

73. A student has to get 40 percent marks to pass an examination. He got 60 marks but fails by 20 marks. Find the maximum
marks of the examination.
a) 150 b) 200 c) 300 d) ) None of these
74. The number of seats in a cinema hall is decreased by 12 percent and the price of tickets also decreased by 4 percent. Find
the change in the collection of revenue.
a) decrease 15.52% b) decrease 16.52%
c) decrease 17.52% d) decrease 14.325

75. A trader marks the price at 8 percent higher than the original price. Due to the hike in demand he again increases the price
by 10 percent. How much percent profit he gets.
a) 17.8% b) 18.8% c) 19.8%
d) 20.8% e) None of these

76. The population of a town is 15000. It increases by 10 percent in the first year and 20 percent in the second year. But in the
third year it decreases by 10 percent. What will be the population after 3 years.
a) 16820 b) 15820 c) 17820
d) 19820 e) None

77. One type of liquid contains 20 percent milk and in other liquid it contains 30 percent milk. If 4 parts of the first and 6 parts
of the second are taken and formed a new liquid A. Find the percentage of milk in third liquid.
a) 26 b) 28 c) 29
d) 30 e) None of these

78. A man has 2000 rupees in his account two years ago. In the first year he deposited 20 percent of the amount in his account.
In the next year he deposited 10 percent of the increased amount in the account. Find the total amount in the account of the
person after 2 years.
a) 2650 b) 2640 c) 2740
d) 2840 e) None of these

79. 1000 sweets need to be distributed equally among the school students in such a way that each student gets sweet equal to
10% of total students. Then the number of sweets, each student gets.
a) 10 b) 12 c) 14 d) 16 e) None

80. If the price of an article is increased by 15%, then by how much the household should decrease their consumption so as to
keep his expenditure same.
a) 13(1/23) % b) 13(2/23)%
c) 11(1/23)% d) 11(2/23)% e) None of these

81. In an election contested by two parties A and B, party A secured 25 percent of the total votes more than Party B. If party
B gets 15000 votes. By how much votes does party B loses the election?
a) 8000 b) 10000 c) 12000
d) 15000 e) None of these
82. A vendor sells 50 percent of apples he had and throws away 20 percent of the remainder. Next day he sells 60 percent of
the remainder and throws away the rest. What percent of his apples does the vendor throw?
a) 20% b) 22% c) 24%
d) 26% e) None of these
83. Alisha goes to a supermarket and bought things worth rupees 60, out of which 40 paise went on sales tax. If the tax rate is
10 percent, then what was the cost of tax free items?
a) 54.60 b) 55.60 c) 56.60
d) 57.60 e) None of these
84. 60 percent of the employees of a company are women and 75% of the women earn 20000 or more in a month. Total
number of employees who earns more than 20000 per month in the company is 60 percent of the total employees. What
fraction of men earns less than 20000 per month?
a) 5/8 b) 5/7 c) 1/5
d) ¾ e) None of these
85. In a library, 30% of the books are in History. 50% of the remaining are in English and 40% of the remaining are in
German. The remaining 4200 books are in regional languages. What is the total number of books in library?
a) 10000 b) 15000 c) 20000
d) 25000 e) None of these

86. A got 30% of the maximum marks in an examination and failed by 10 marks. However, B who took the same examination
got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the
examination?
a) 65 b) 75 c) 80
 d) 90 e) None of these

87. The population of a town is 15000. It increases by 10 percent in the first year and 20 percent in the second year. But in the
third year it decreases by 10 percent. What will be the population after 3 years?
a) 16820 b) 15820 c) 17820
d) 19820 e) None of these

88. 30 litre of solution contains alcohol and water in the ratio 2:3. How much alcohol must be added to the solution to make a
solution containing 60% of alcohol?
a) 10 b) 12 c) 14
d) 15 e) None of these

89. 2000 sweets need to be distributed equally among the school students in such a way that each student gets sweet equal to
20% of total students. Then the number of sweets, each student gets.
a) 50 b) 100 c) 20 d) 150 e) None

90. A reduction of 20% percent, in the price of rice enables a housewife to buy 5 kg more for rupees 1200. The reduced price
per kg of rice?
a) 36 b) 45 c) 48
d) 60 e) None of these

91. The population of a village has increased annually at the rate of 20%. If at the end of 3 years it is 21600, the population in
the beginning of the first year?
a) 10000 b) 12500 c) 15000
d) 17500 e) None of these

92. 12% of the voters in an election did not cast their votes. In this election there are only two candidates. The winner by
obtaining 45% of the total votes and defeated his rival by 2000 votes. The total number of votes in the election?
a) 50000 b) 75000 c) 100000
d) 125000 e) None of these

93. 25% of candidates who appeared in an examination failed and only 450students qualify the exam. The number of students
who appeared in the examination was:
A) 700 B) 600 C)550 D)500

94. The strength of a school increases and decreases in every alternate year by10%. It started with increase in 2000, then the
strength of the school in 2003 as compared to that in 2000 was:
A) increased by 8.9% B)decreased by 8.9% C)increased by 9.8% D)decreased by 9.8%

95. The population of a town increase by 5% every year. If the present population is 9261. The population 3 years ago was:
A) 5700 B) 6000 C)7500 D)8000

96. The dozen pairs of earrings quoted at Rs.180 are available at discount of 20%. How many pairs of earrings can be bought
for Rs. 48?
A)3 Pairs B)4 pairs C)2 pairs D)5 pairs

97. Ram saves 14% of his salary while Shayam saves 22%. If both get the same salary and Shyam saves Rs. 1540, What is
savings of Ram?
A) 990 B) 980 C)890 D)880

98. There is a ratio of 5:4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second
number?
A) 12 B) 24
C)18 D)Data Inadequate

LOD-1
1. If the side of a square is increased by 30%, its area is increased by:
(a) 9% (b) 30% (c) 60% (d) 69%
2. The price of a machine increases by 20% in a year and decreases by 15% in the following year. What is
net percentage increase/decrease in the price of the machine?
(a) 1% increase (b) 2% increase (c) 1% decrease (d) 2% decrease
3. In an election between two candidates one got 55% of the total valid votes and 20% of the total votes
 casted are invalid. If the total votes are 7,500, then what is the number of valid votes that the other
person got?
(a) 2,000 (b) 2,500 (c) 2,700 (d) None of these
4. From 2007 to 2010, Vijay got a hike of 20% in his salary every year except in 2008 in which he got a
reduction of 20%. If his salary in 2006 was Rs. 6.25 lakh per annum, what was his approximate annual
salary (in lakhs) in 2010?
(a) 8.84 (b) 6.76 (c) 10.64 (d) 8.64
5. The price of petrol is increased by 25%. By what percent should a car owner reduce the consumption of
petrol so that his expenditure on petrol remains constant?
(a) 25 (b) 30 (c) 50 (d) 20

6. The ratio of income and expenditure of a person is 4 : 3. If income is increased by 20% and expenditure
is decreased by 10% then what is the percentage increase or decrease in the savings?
(a) 110% (b) 119.7% (c) 100% (d) 80%

7. 75% of a number when added to 75 is equal to the number. The number is :

(a) 150 (b) 200 (c) 225 (d) 300

8. If Ajay’s income is 30% more than Rajeshs income, then Rajesh’s income is how much percent less
than Ajay’s income?
(a) 39 1 % (b) 23 1 % (c) 26 1 % (d) 241 %
13 13 13 7

9. x is 5% of y, y is 24% of z. If x = 480, then the value of z is

(a) 30000 (b) 35000 (c) 40000 (d) 45000

10. If X’s income is 25% more than Y’s and Y’s income is 20% more than Z’s, by what percentage is
X’s income more than Z’s?
(a) 25% (b) 33.33% (c) 50% (d) None of these

11. 52.8% of 400 = 80% of x. Find the value of x.

(a) 528 (b) 184 (c) 185 (d) 264

12. Girish had three books P, Q and R. Of these, P had 150 pages, Q had 20% more pages than P and R had
20% less pages than P. If he removed 10%, 5% and 15% of pages from P, Q and R respectively, then
what percentage of the total pages did he tear?
(a) 9% (b) 10% (c) 10.33% (d) 9.33%

13. Ranjan’s income is 20% more than Jeewan’s income and their expenses are 70% and 60% of their
respective incomes. By what percentage is Ranjan’s saving more/less than Jeewan’s?
(a) 11.11 (b) 10 (c) 12 (d) 13

14. In an exam, the ratio of marks obtained by A and B is 9: 11. If the sum of 22.22% of A’s marks and
27.27% of Bs marks is 115, then what is the sum of marks obtained by A and B in the exam?
(a) 420 (b) 529 (c) 460 (d) 480

15. A survey shows that 74% of the Indians like apples whereas 68% like oranges. What percentage of
Indians like both apples and oranges (If every Indian likes at least one of them)?
(a) 30% (b) 34% (c) 42% (d) 50%

16. If 70% of the total students in a school are boys and the number of girls in the school is 534, then the
number of boys is:
(a) 1246 (b) 1008 (c) 1208 (d) 3024

17. The price of diesel goes up by 20%. So Mehta reduces his consumption to such a level that his
expenditure increases by only 12%. By what percentage has he reduced the consumption?
(a) 6.5% (b) 6.67% (c) 6.9% (d) 7.2%

18. 200 students took the board examination in a school, and 13% of the students got distinction. The
number of boys who got distinction is 2 more than the number of girls who got distinction. If 20% of
the girls got distinction, the total number of boys in the school is
(a) 160 (b) 150 (c) 140 (d) 175

19. In a class of 32 students, 4 students were absent on a day. Among the students who were present on that
day, 25% had failed in mathematics test. How many students were present in the class on that day who
had passed that mathematics test?
(a) 16 (b) 21 (c) 12 (d) 18
 20. Murali has a certain number of mangoes, 15% of which are rotten. He gives 60% of the remaining to his
friend and is left with 102 fresh mangoes. How many mangoes did he have in the beginning?
(a) 300 (b) 150 (c) 600 (d) 450

LOD-2
1. The income of A is 20% more than B and their expenditures are 60% and 70% respectively of their
incomes. By what percentage is the saving of A is more than that of B?
(a) 30% (b) 60% (c) 50% (d) Cannot be determined

2. Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges
or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of
oranges he can buy is
(a) 25 (b) 18 (c) 20 (d) None of these

3. Dry grapes contain 10% water whereas fresh grapes contain 75% water. To obtain 15 kgs of dry grapes,
how many kgs of fresh grapes are needed?
(a) 54 kgs (b) 20 kgs (c) 150 kgs (d) 112.5 kgs

4. In an Opinion Poll conducted among all voters, 60% of the voters claimed that they would vote for
candidate A and the rest claimed that they would vote for candidate B. But on polling day x% of each
candidate's supporters changed their mind and voted for the other candidate, which resulted in both
candidates securing equal votes. Find the value of x.
(a) 10% (b) 20% (c) 40% (d) 50%

5. Since the prices of petrol increased by 10%, I changed my car to a more efficient model which gave 20%
more mileage per litre of petrol. If I continue to travel the same distance, by what percent does my
expenditure change?
(a) Increases by 32% (b) Decreases by 12%
(c) Increases by 9.09% (d) Decreases by 8.33%

6. In the production of a watch, labor charges account for 25% of the cost and the rest of the cost is material
cost. If the cost of material increases and now it accounts for 80% of the total cost of the watch, find the
percentage increase in the cost of material.
(a) 6.66% (b) 16.66% (c) 20% (d) 33.33%

7. The engine of a car accounts for 20% of the car's cost. The cost of the engine increases by x% and
consequently the cost of the car also increases by the same amount as the increase in engine's cost. Now
the cost of the engine accounts for 25% of the car's cost. Find the value of x%.
(a) 20% (b) 25% (c) 33.33% (d) 40%

8. NMAT is an objective type paper of 200 questions with 1 mark for each correctly answered question and
no negative marks for wrong answers or questions left un-attempted. If Shiplu had attempted 60% more
questions than he did and had made 20% fewer errors than he did, his score would have increased by
100%. What percent of the questions attempted by Shiplu are correct?
(a) 25% (b) 33.33% (c) 40% (d) 66.66%

9. Two sites were bought simultaneously, one in city A and the other in city B at a cost of 4 lakhs and 9
lakhs respectively. The one bought in city A appreciates by x% every year for 2 years and then
depreciates byx% for the next 2 years. The other depreciates by x% for 4 years. What is the value of x if
at the end of 4 years, both the sites have the same value?
(a) 10% (b) 20% (c) 25% (d) 30%

10. K. Bedi and A. Kejriwal contest an election. At the election 10% of the people on the voting list did not
vote and 60 votes recorded were rejected as illegal. The margin by which A. Kejriwal won was 308 and it
was found he had been supported by 47% of the whole number on the voters list. What was the number of
legal votes recorded?
(a) 2914 (b) 2606 (c) 5580 (d) 5520

ALP (ADVANCED LEVEL PROBLEMS)

1. 2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the
voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q and P lost
by 50 votes. Then the total number of voters is ________
2. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was
half more than what I had paid. What percent of the total paid by one was paid for the pens? (1996)
(a) 37.5% (b) 62.5% (c) 50% (d) None of these

In any given month, a salesman earns a commission of a% on the first ₹1000 worth of his sales. He earns b% on all
further sales during that month. He made a commission of ₹900 from the sales of ₹3000 in January and ₹1300 from
the sales of ₹4000 in February. Find the value of a.

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum
returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with
others.

Option A: Invest in a public sector bank. It promises a return of +0.10%.

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall
will entail a return of –3%.

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall
will entail a return of +2%.

4. The maximum guaranteed return to Shabnam is (2007)

(a) 0.30% (b) 0.25% (c) 0.10% (d) 0.20% (e) 0.15%

5. What strategy will maximize the guaranteed return to Shabnam? (2007)

(a) 30% in option A, 32% in option B and 38% in option C
(b) 100% in option A
(c) 36% in option B and 64% in option C
(d) 64% in option B and 36% in option C
(e) 1/3 in each of the three options

6. A leather factory produces two kinds of bags, standard and deluxe bag. The profit margin is Rs 20 on a standard
bag and Rs 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times
per bag on the two machines are as follows:

The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following
production plans, which one meets the machine availability constraints and maximizes the profit? (2003C)
(a) Standard 75 bags, Deluxe 80 bags
(b) Standard 100 bags, Deluxe 60 bags
(c) Standard 50 bags, Deluxe 100 bags
(d) Standard 60 bags, Deluxe 90 bags.

7. At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the
beginning of the year and sold q % of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine
dozen goats at the end of year 2002, after making the sales for that year, which of the following is true? (2003C)
(a) p = q (b) p < q (c) p > q (d) p = q/2

8. A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs 600
from the people already solicited. The people already solicited represent 60% of the people, the college will ask for
donations. If the college is to raise exactly the amount needed for the new building, what should be the average
donation from the remaining people to be solicited? (2001)
(a) Rs 300 (b) Rs 250 (c) Rs 400 (d) Rs 500

9. A jewellery shop owner conducts his business in the following manner. Every once in a while he raises his prices
by a certain percentage and a while later he reduces his prices by the same percentage. After one such updown cycle
of increasing and then decreasing his price by x%, the price of a jewel decreases by ₹100. In the next cycle, he
increases and then decreases his price by (x/2)% and then sells the jewel for ₹2376. What is the initial price of the
jewel (in ₹)?
(A) 2450 (B) 2475 (C) 2500 (D) 2575
The following graph represents the variable cost of widgets as a function of quantity produced. The cost of
production has two components, variable cost — which is given in the graph, and fixed cost — which is Rs 800 for
the first shift in which 30 widgets can be produced and if more production is desired then a second shift is started
which can produce an additional 30 widgets. The fixed cost of the second shift is Rs 1200. Average cost is defined as
the total cost / total number of the widgets
Marginal cost is defined as change in total cost / change in number of widgets produced.

10. What is the average cost if number of widgets in July is 40? (2000)
(a) 110 (b) 140 (c) 3600 (d) 180

11. If the number of widgets increase form 40 in July to 41 in September what is the marginal cost?
(a) 110 (b) 130 (c) 170 (d) 150

12. What is the total cost of production in July? (2000) (a) 3600 (b) 5600 (c) 6400 (d) 4300

13. What number of widgets give the maximum profit? (2000) (a) 30 (b) 40 (c) 25 (d) 60

14. What number of widgets being 0-60 which of the following is true? (2000)
(a) The average cost increases consistently
(b) The average cost decreases consistently
(c) The average cost decreases till minimum then increases
(d) The average cost increases till maximum then decreases

A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the
total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German Mark
increased by 30% and that of USA Dollar increased by 22%. Due to market conditions the selling price cannot be
increased beyond 10%. Then

15. What is the maximum current gain possible? (1998)

(a) 10% (b) 12.5% (c) 0% (d) 7.5%

16. If the USA Dollar becomes cheap by 12% over its original cost and the cost of German Mark increased by 20%.
The selling price is not altered. What will be the gain? (1998)
(a) 10% (b) 20% (c) 15% (d) 7.5%

17. In a company 40% are male, out of which 75% earn a salary of 25,000 plus. If 45% of the employees earn 25,000
plus salaries, what is the fraction of female employees earning less than or equal to 25,000? (1999)
(a) 1/4 (b) 3/7 (c) 3/4 (d) 5/9

Ghosh Babu has a certain amount of property consisting of cash, gold coins and silver bars. The cost of a gold coin is
Rs. 4000 and the cost of a silver bar is Rs. 1000. Ghosh Babu distributed his property among his daughters equally.
He gave to his eldest daughter gold coins worth 20% of the total property and Rs. 25000 in cash. The second
daughter was given silver bars worth 20% of the remaining property and Rs. 50000 cash. He then gave each of the
third and fourth daughters equal number of gold coins and silver bars both together accounting each for 20% of the
property remaining after the previous distribution and Rs. 25000 more than what the second daughter had received in
cash.

18. The amount of property in gold and silver possessed by Ghosh Babu is
(a) Rs.2,25,000 (b) Rs.2,75,000
(c) Rs. 4,25,000 (d) None of these

19. Total property of Ghosh Babu (in Rs.lakh) is

(a) 5.0 (b) 7.5 (c) 10.0 (d) 12.5.

20. If Ghosh Babu had equal number of gold and silver bars, the number of silver bars he has is
(a) 90 (b) 60 (c) 75 (d) 55

21. Vaibhav was writing the CAT exam. There were four passages of equal length (in words) and they had 5, 8, 8 and
6 questions respectively. Vaibhav can answer exactly 12 questions in the time he takes to read any one of the four
passages. Assume that his rate of reading and answering question remains the same across all four passages. By what
rate should Vaibhav increase his reading speed in order to cutdown his total time spent by 10%?
(1) 20% (2) 18.5% (3) 25% (4) 9.8%

Two candidates Ram and Rajat are appearing for an examination. Each question correctly answered
fetches 1 mark while for every wrong answer 1 mark is deducted. The examination has a fixed pass mark.
Ram attempts a certain percentage of questions and gets 10% of his attempts wrong. Consequently, he
secured a net score of 64% of the total which is 22 marks more than the pass mark. Rajat attempts a
different percentage of questions and gets 20% of his attempts wrong. Consequently, he secures a net
score of 54% of the total and passes by 12 marks.

22. What percentage of the total questions did Rajat attempt? _______%

23. What is the pass mark?

24. The quantities V, x, y, z, a and b are related as follows: V = 2xyz + 3ab. If x, y, z, a, b change by +25%,
+60%, –10%, +20% and +50%, what is the percentage increase in V?
(A) 60% (B) 80%
(C) 92% (D) Cannot be determined

ANSWER KEY

Percentage Change, Change of Base, Successive Percentage Change:

1. b 6. a 11. b 16. a
2. b 7. b 12. a 17. b
3. b 8. c 13. d 18. b
4. a 9. c 14. c 19. c
5. b 10. b 15. b 20. b
 LOD-1
1. d 6. a 11. d 16. a
2. b 7. d 12. d 17. b
3. c 8. b 13. b 18. c
4. d 9. c 14. c 19. b
5. d 10. c 15. c 20. a

LOD-2
1. b 6. d
2. c 7. c
3. a 8. d
4. d 9. b
5. d 10. d

ALP
Answers:
1. 2500 9. C 17. C
2. B 10. B 18. B
3. 10 11. D 19. A
4. D 12. B 20. D
5. C 13. C 21. 2
6. A 14. C 22. 90%
7. C 15. A 23. 42
8. A 16. B 24. B