Percentage based CAT level Questions Exercise B for Mains Exams

Exercise B

 1. A motorist decreases his distance covered annually (in km) by 10% when the price of petrol is increased by 3%. Find the percentage change in petrol bill. 


2. The rate of increase of the price of rice is observed to be 3 per cent more than the inflation rate expressed in percentage. The price of rice on January 1, 2008 is Rs. 25/kg. The inflation rates of years 2008 and 2009 are expected to be 13% each. The expected price of rice on January 1, 2010 would be. 


3. Ganesh can buy 40 oranges or 50 mangoes. He retains 10% of the amount for bus fares and buys 20 oranges and of the balance. How many mangoes can he purchase ? 


4. Raju bought 5 erasers, 4 pencils and 7 pens. Sonali bought 9 pens, 10 erasers and 8 pencils for an amount which was half more what Raju had paid. What per cent of the total paid by Raju were paid for the pens ? 


5. In a survey of children education, 90% of those asked are in the favour of at least one of the proposal : I, II and III, 48% of those asked favoured proposal I, 36% favoured proposal II and 16% favoured, proposal III. If 5% of those asked favoured all three of the proposals. What percentage of those asked favoured more than one of the three proposals ? 


6. Jyoti took five papers in an examination where the full marks were for each paper, her marks in these papers were in proportion of 2 : 3 : 4 : 5 : 6. In all papers together, the candidates obtained 50% of the total marks then what is the number of papers in which she got more than 40% marks ? 


7. One bacteria splits into eight bacteria of the next generation. But due to unfavorable conditions only 25% of one generation can produce the next generation. If the fourth generation number is 64 millions. What is the number in first generation ? 


8. Sixty per cent of the employees of a TCS company are men and 40% of them are earning more than Rs. 40,000 per year. If 40% of the company’s employees earn more than Rs. 40,000 / year. What fraction of the women employed by the company earn Rs. 40,000 /year ? 


9. In a factory there are four types of machines x, y, z and A which produces 10%, 20%, 75% and 25% of the total products respectively. Machines x, y, z and A produces 1%, 4%, 5% and 6% defective products respectively. What is the percentage of non-defective products ? 


10. Each edge of a cube is increased by 25%, then the percentage increase in surface area of the cube is ? 


11. The boys and girls in a college are in the ratio 4 : 5. If 40% of boys and 35% of the girls are adults, the percentage of students who are not adults is ?

 12. Given series is 1 + 4 + 9 + 16 + 25 + 36 + ………. . What is the percentage of 10th term relative to 15th term ? 


13. A driver reduces his distance covered annually (in km) by 25% when the price of petrol is increased by 5%. Find the per cent increase/ decrease in his annual petrol bill ? 


14. In an election 8% of the people in the voter’s list did not participate and 48 votes were declared invalid. There are only two candidates Shyam and Krishna. Shyam defeatedKrishana by 440 votes. It was found that 60% of the people listed in the voter’s list voted for Shyam. Find the total number of votes polled. 


15. The rate of increase of the price of coal is observed to be five per cent more than the inflation rate expressed in %. The price of coal, on March 4, 2008 is Rs. 100 / tonnes. The inflation rates of years 2008 and 2009 are expected to be 10% each. Find the expected price of coal on March 4, 2009. 


16. The number of votes not cast for the Samata Party increased by 20% in the general election over those not cast for it in the previous assembly polls and the Samata Party lost by a majority thrice as large as that by which it had won the assembly polls. If a total 3,60,000 people voted each time, how many voted for the Samata Party in the previous assembly polls ? 


17. Gita buys 25 red pens or 50 blue pens. She retains 20% for autorikshaw as fares and buys 10 red pens and of the balance. She purchases blue pens. What is the number of blue pens she can purchase ? 


18. Raj Shekhar bought 3 books, 4 pencils and 5 chocolates while Sonali bought 12 books, 16 pencils and 16 chocolates for an amount which was thrice and half more what Raj Shekhar had paid ? What percentage of the total paid by Raj Shekhar was paid for chocolates ? 


19. In a survey of political preferences, 80% of those asked were in favour of at least one of the proposals I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 4% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals ?


20. Riya took five proposals in an examination where the full marks were for each paper her marks in these papers were in proportion of 4 : 3 : 5 : 6 : 7. In all papers together, the candidates obtained 60% of the total marks. Then what is the number of papers in which she got more than 50% marks ? 


21. Mr. Ivan Royston is working in the Max New York Life Insurance (MAX). He was hired on the basis of commission and he get the bonus only on the first years commission. He got the policies of Rs. 4 lakh having maturity period of 10 years. His commission in the first, second, third, fourth, and for the rest of the years is 25%, 20%, 10%, 8% and 5% respectively. The bonus is 30% of the commission. If annual premium is Rs. 40,000, then what is his total commission if the completion of the maturity of all the policies in mandatory ? 


22. A person gives 20% to his wife and 15% of the remaining to a hospital (as a donation) again 10% of the remaining to Prime Minister’s RetiredFund. Then he has only Rs. 8,400 with him. What was the initial sum of money with that person ? 


23. Find the percentage of the quantity 13 + 23 + 33 + 43 + 53 with respect to 13 + 23 + 43 + 53 + 63 + 73 . 


24. If a cone and a cylinder have the same height and radius. What is the percentage difference in volume of cone relative to cylinder ? 


25. A resistor of length l and cross sectional area A. If it is cut in four part across the length. Find the % change in resistance of the resistor. 


26. A wire of length l and cross-sectional area A. If its length increase by 20% and its cross-sectional area increases by 10%. Find the percentage change in the resistance of the wire. 


27. A box of wood of thickness 2 cm. If outer dimensions of the box 24 × 20 × 16 cm3 . How much per cent of air occupied inside the box ?

Percentage Based Questions CAT level for Bank exams 2017

25. Ramesh gets a lumpsum amount of retirement. First he spends 70% to buy a house 33% of the remained, he spends on his daughter’s marriage from the balance he invest 60% in a business and finally he is left with Rs. 2,25,500. How much did he get on retirement ? 

26. The price of a saree is reduced by successive discounts of 10% and 15%. Find the net percentage decrease in price. 27. The price of a Maruti car is first increased by 12% and later on reduced by 10%. If the original price was Rs. 4,00,000. What is the final price and the % change in the price ? 

28. In an election between two candidates 60% of the votes cast their votes, out of which 5% of the votes were declared invalid. A candidate got 17,100 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election. 

29. Roma’s Mathematics test had 75 problems, i.e. 10 Arithmetic, 30 Algebra and 35 Geometry problems. Although she answered 60% of arithmetic, 50% of the algebra and 40% of the Geometry problems correctly. She did not pass the test because she got less than 60% of the problems correct. How many more questions she would have needed to answer correctly to score a 60% passing grade ? 

30. If 80% of (x – y) = 50% (x + y), then what per cent of x is y ? 

31. A salesman’s commission is 5% on all sales upto Rs. 10,000 and 4% on all sales exceeding this. He remits Rs. 31,100 to his parent company after deducting his commission. Find the total sales of salesman. 

32. Radha spends 80% of her income. After a increment, her income is increased by 40% and she also increased her expenditure by 35%. Find the percentage increase in savings. 

33. The weight of the container alone is 25% of the container filled with a certain fluid when some fluid is removed, the weight of the container and remaining fluid is 50% of the original total weight. What fractional part of the liquid has been removed ? 

34. In a competitive examination in stage X, 10% candidates got selection from the total appeared candidates. Stage Y had an equal number of candidates appeared and 12% candidates got selected with 80 more candidates got selected than X. What was the number of candidates appeared from each stages ? 

35. The price of maruti is Rs. 10,00,000. It was insured to 90% of its price. The maruti was damaged completely man’s accident and the insurance company paid 80% of the insurance. What was the difference between the price of maruti and the amount received ? 

36. A bag contains 800 coins of 25 (Paise) denomination and 1500 coins of 50 (Paise) denomination. If 12% of 25 (Paise) coins and 24% of 50 (Paise) coins are removed. The percentage of money removed from the bag is nearly ? 

37. A reduction of 20% in the price of rice enables a person to buy 10 kg more for Rs. 100. What is the reduced price / kg. 

38. A reduction of 30% in the price of wheat enables a person to buys 3 kg. more for Rs. 90. Find the original price of wheat / kg. ? 

39. A class has girls and boys in the ratio 2 : 3. Among the girls, the ratio of Mathematics to Physics students is 4 : 5. If the ratio of Mathematics and Physics students in the entire class is 1 : 2. What percentage of class comprises girls studying Mathematics ? 

40. If X2 % of Y = Y2% of Z. And Z4 % of X = Y% of Y. Find the relation between X and Y. 

41. One type of liquid contains 30% of water and the second type of liquid contains 40% of water. A glass is filled with 10 parts of first liquid and 6 parts of second liquid. What is the percentage of water in the new mixture in the glass ? 

42. Due to an increase of 30% in the price of eggs, 3 eggs less are available for Rs. 7·80. What is the present rate of eggs per dozen ? 

Percentage Based Questions CAT Level for All Mains Exams 2017

1. The population of Delhi is 40,00,000 it increases at the rate of 10% per annum. What was its population 2 years ago and also what will be its population after 2 years ?

2. The population of a city is 25,000. If increased by 15% during first year. During second year it decreased by 25% and increased by 40% during the third year. What is the population after 3 years ?

3. The tax on a commodity is diminished by 2.5% and its consumption increases by 5%. Find the effect on revenue ?
Ans :Let A be tax on a commodity and B be the consumption.

Now, new revenue = tax × consumption

(1 - 2.5/100)A . (1+5/100)B

97.5/100 * 105/100 AB
Effect on revenue = x + y + xy/ (100 × 100)
 = – 2·5 + 5 – 5 × 2·5/ (100 × 100)
 = 2·5 – 5 /4000
 = 2·5 – 0·00125
= 2·5

4. In an examination 75% students failed in Economics, 55% failed in Maths and 35% failed in both the subjects and 500 passed in both the subjects. Find the total number of students.
By using formula :
% of students who passed in both subjects = [100 – (x + y – z)] % = [100 – ( 75 + 55 – 35)]%
= (100 – 95 )% = 5%
Since, 5 % students = 500 students
 ⇒ 100% (5 × 20) students = 500 × 20 = 10,000 students.

5. There are 500 students in an examination 85% students passed in Geography and some of the students passed in Civics while 65% students passed in both the subjects. If 300 students failed in both the subjects. Find the % of students who passed in Civics.

Solution : Let the required % of students who passed in Civics is x.
Now, by using Set Theory formula n (A ∪ B) = n (A) + n (B) – n (A ∩ B)
No. of students passed in one or both the subjects = x% + 85% – 65% = (x + 20)%
No. of students passed one or both the subjects = (x + 20) %
Now, Number of students failed = [100 – (x + 20)]% = (80 – x)%
Since, in 100 students, (80 – x) students is failed
∴ In 500 students, 80 – x 100 × 500 students is failed According to questions— 80 – x 100 × 500 = 300
∴ 80 – x = 60; x = 80 – 60 = 20 Required % of students who passed in Civics = 20.

5. In an examination a candidates scores 35% but fails by 45 marks. If the passing marks is 65%. What is the maximum marks ?
Let the maximum marks = 100
 Secured marks = 35
Passing marks = 65
 Difference = 65 – 35 = 30
 When he fails by 30 marks maximum marks = 100
∴ He fails by 1 marks, maximum marks = 100 30
 ∴ He fails by 45 marks maximum marks
= 100 /30 × 45 = 150.

6. The maximum marks in Civics is 120. A candidates scores 60 marks but fails by 12 marks. What is the percentage pass marks ?

Since candidates get total (60 + 12) marks
∴ Candidates get 72 marks out of 120 marks i.e., In 120 marks,
candidates get 72 marks
∴ In 100 marks, candidates get 72 120 × 100%
Hence, percentage pass marks = 60%.

7. Gita and Reeta appears for an examination. Gita scores 40% and fails by 24 marks. While Reeta scores 45% which is 16 marks more than the pass marks. What are the maximum marks ?
Let the maximum marks = M Gita gets pass marks = 40 /100 M + 24
While Reeta gets pass marks = 45 /100 M – 16
Since, both are equal, So,
 40/ 100 M + 24 = 45 /100 M – 16
 or 40 = 5 100 M
 ∴ M = 800.

8. In a school library, 25% books are in Hindi, 80% of the remaining are in English and the remaining 9,000 are in various languages. What are the total number of books in English ?
Let the total books in Library = 100
Now, books in Hindi = 25
Books in English = 75 × 80/ 100 = 60
Remaining books = 100 – (25 + 60) = 15
When remaining books are 15, then total books = 100
 ∴ If remaining books are 9,000, then total books
= 100 /15 × 9,000 = 60,000

9. An Army lost 25% of its men in war, 10% of the remaining due to diseases and 5% of the rest declared war disabled. Thus, the strength was reduced to 6,41,250 active men. Find the original strength.
Let the original strength = 100
Due to war lost men = 25
Due to diseaseslost men = 75 × 10 /100 = 7·5
Disabled men = (75 – 7·5) × 5 /100
= 3·375
Reduced strength = 100 – (25 + 7·5 + 3·375) = 64·125
When 64·125 is active then original is 100. 6,41,250 is active men,
 then original strength = 10,00,000.

Exercise A 

1. If 121 2 % and 5% of a number is 550 and 220. Find the number. 


2. If the sum of numbers obtained by taking percentage of 25% and 10% of a certain number is 350. Find the certain number ? 


3. The difference between the numbers obtained by increasing a certain number by 2% and that obtained by diminishing it by 1·5% is 350. Find the original number ? 


4. P% of a number C is equal to Q% of a number D. Find the per cent of C relative to D ? 


5. The sum of two numbers is A. Seven times of greater number exceeds five times of the smaller one by kA. Find what per cent the greater number is more than the smaller one ? 


6. A shopkeeper marks prices at 121 2 % higher than the original price. Due to increase inflation he further increases the price by 6 1 2 %. How much % profit will he get ?


 7. The price of rice is increased by 40%. Find how much per cent its consumption must be decreased if expenditure remains constant ? 


8. The price of wheat decreases by 24·5 %. Find by how much per centits consumption must be increased if expenditure remains constant ? 

9. The price of kerosene decreases by 25%. Find how much per cent must its consumption be increased if expenditure remains constant ? 


10. The population of Bombay was 15,00,000, 3 years ago. If population increased by 10% during first year, decreased by 5% during the second year and again increased by 15% during the third year. What is its population now ? 


11. In a factory, the present price of a machine is Rs. 75,000. What was its price 2 years ago and will be its price 2 year hence. If annual rate of depreciation of the machine is 20%. 


12. In an election be two candidates Ram and Rahim, Ram got 40% of the votes polled and is defeated by 1600 votes. Find the number of votes polled for Rahim.


13. An ore contains 35% of mass as impurity, whole the metal extracted from this ore contains 5% impurity. How much metal will 240 tonnes of the ore yield ?


14. In April, a cricket team that played 70 games had won 40% of its games. After a phenomenal arising streak this team raised its average to 60%. How many games the team have won in a row to attain this average ? 


15. Sheela’s income increases by Rs. 2,000 but the rate of tax being reduced from 15% to 12%. She pays the same amount of tax as before. What is her increased income, if 10% of her income is exempted from tax in both the cases ?


16. Two numbers are 20% and 25% less than a third number. How much % is the second number less than the first ? 


17. A reduction of Rs. 2/kg enables a man to purchases 8 kg. more sugar for Rs. 32. Find the original price of rice. 


18. A reduction of 60% in the price of chocolates enables a person to buy 10 kg. more for Rs. 240. Find the original price of chocolates per kg. 


19. A two digital number obtained by after interchanging the initial number increases by 9. What is percentage increase in number, if the sum of numbers is 3 ? 


20. ‘A’ spends 75% of his income and saves the rest. When the cost of living increased, his expenses increased by 251 2 % and his income also increased by 121 2 %. What percentage of his income does he save now ? 


21. If the length of a rectangle is increased by 60% and the breadth is decreased by 40%, then find the % change in area of the rectangle. 


22. Nitin’s contributions to charity, religious donation and community welfare are in the ratios of 10 : 20 : 40 respectively. Express the contribution in percentage terms. 


23. Which is greatest in 50 2 % 0·3, 2 15 ? 


24. Gita’s salary is 20% less than Sita’s salary but 30% more than Rita’s salary. If Rita’s salary is Rs. 75 less than Sita’s salary, find the salary of each.

Next Chapter is on Averages

Problems on ages

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A.	8, 20, 28	B.	16, 28, 36
C.	20, 35, 45	D.	None of these

Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

A.	2 years	B.	4 years
C.	6 years	D.	8 years

A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A. 32 years B. 36 years C. 40 years D. 48 years

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age?

A. 1 year B. 2 years C. 25 years D. Data inadequate E. None of these

The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is:

A. 5 : 2 B. 7 : 3 C. 9 : 2 D. 13 : 4

1. The average age of two girls and their father is greater than the average age of those two girls and their mother by 3 yr. The average age of the four is 19 yr, If the average age of the two girls be 5.5 yr, then find the age of the father. 

(a) 27 yr 

(b) 37 yr 

(c) 47 yr 

(d) 57 yr 

(e) None of these

2. The average age of 54 boys in a class was calculated as 14 yr. It was later realized that the actual age of one of the boys in the class was 12 yr but it was calculated as 13 yr. What is the actual average age (round off) of the boys in the class? 

(a) 8 yr

(b) 10 yr

(c) 12 yr

(d) 14 yr

(e) 16 yr

3. Rajesh decides to marry 5 yr after he gets a job. He was 17 yr old when he passed class 12th. After passing class 12th, he had completed his graduation course in 3 yr and PG course in 2 yr. He got the job exactly 1 yr after completing his PG course. At what age will he get married? 

(a) 22 yr

(b) 24 yr

(c) 26 yr

(d) 28 yr

(e) 30 yr

4. The average age of 9 students and their teacher is 18 y. The average age of the first four students is 19 yr and that of the last five is 10 yr. The teacher’s age is 

(a) 36 yr

(b) 34 yr

(c) 54 yr

(d) 58 yr

(e) 64 yr

5. Ramesh’s present age is three times his son’s and nine-thirteenth of his father’s present age. The sum of the present ages of all three of them is 125 yr. What is the difference between the present ages of his son and father?

(a) 30 yr

(b) 35 yr

(c) 40 yr

(d) 45 yr

(e) None of the above 

6. The ratio of the present age of  Waqar and  Makrand is 11 : 3. Waqar is 12 yr younger than Rahim.  Rahim’s age after 7 yr will be 85 yr. What is the present age of Waqar’s father, who is 20 yr older than Waqar?  

(a) 46yr

(b) 67yr

(c) 86yr

(d) 89yr

(e) None of these 

7. The average age of a family of five members is 28. If the present age of the youngest member is 8 yr, what was the average age of the family at the time of the birth of the youngest member? 

(a) 12 yr

(b) 16 yr

(c) 20 yr

(d) 24 yr

(e) None of these 

8. At present, Prakhar is three times Akhil’s age. After 7 yr, Prakhar will be twice Akhil’s age, then how many times will Prakhar’s age be in another 14 yr time with respect to Akhil’s age then? 

(a) Same for both

(b) 2

(c) 1.5

(d) 3

(e) 4

9. The present age of Rahul’s father is four times Rahul’s present age. Five years back Rahul’s father was seven times as old as Rahul was at that time. What is the present age of Rahul? 

(a) 6 yr

(b) 9 yr

(c) 10 yr

(d) 15 yr

(e) 20 yr

10. Ramesh’s brother is 3 yr elder to him. His father was 28 yr of age when his sister was born, while his mother was 26 yr of age when he was born. If his sister was 4 yr of age when his brother was born, the age of Ramesh’s mother when his brother was born was

(a) 23yr

(b) 29yr

(c) 33yr

(d) 39yr

(e) 43 yr

More Questions Are Updated Soon 

Quant Single Items

1. A certain fraction is equivalent to 2/5 . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3 . What is the sum of numerator and denominator of the original fraction? 
(1) 49 
(2) 35 
(3) 28 
(4) 26 
(5) 21


2. The population of city X increased from 650,000 in 2000 to 700,000 in 2010, and it is projected that the population will increase by the same number from 2010 to 2020. Approximately what is the projected percent increase in population from 2010 to 2020 ? 
(1) 7.1% 
(2) 7.7% 
(3) 8.3% 
(4) 14.3% 
(5) 15.3%


4. In how many different ways, letters of the word MANPOWER be arranged such that all vowels are together? 
(1) 360 
(2) 4320 
(3) 1440
(4) 2160
(5) 40320

5. On a certain test, 3 students each had a score of 90, 9 students each had a score of 80, 4 students each had a score of 70, and 4 students each had a score of 60. What was the average (arithmetic mean) score for the 20 students ? 
(1) 70.5 
(2) 75.0 
(3) 75.5
(4) 80.0 
(5) 80.5

Direction (6 – 10) : Study the following Pie-chart carefully and answer the questions given below:
Survey Conducted on 21000 people to find out various Professionals in the town and percentage of Female Professionals amongst them Various Professionals = 21000

Profession	% of Females
Lawyers	40
Teachers	80
Architects	40
Engineers	60
Designers	35
Doctors	20

6. What is the ratio of the number of male Architects to the number of male Teachers in the town?
(1) 11 : 5
(2) 3 : 2
(3) 5 : 11
(4) 2 : 3
(5)None of these

7. Female Doctors are what percent of total number of male and female professionals in the town?
(1) 4.2
(2) 2.8
(3) 1.5
(4) 3.5
(5)None of these

8. What is the difference between the total number of male and female professionals in the town?
(1) 2568
(2) 2268
(3) 2108
(4) 2328
(5)None of these

9. The total number of Lawyers in town is approximately what percent of doctors in the town?
(1) 95
(2) 98
(3) 90
(4) 85
(5) 81

10. What is the ratio of total number of male Engineers and Designers to the female professionals in the town?
(1) 41 : 44
(2) 55 : 53
(3) 31 : 35
(4) 444 : 35
(5)None of these


ANSWERS
61. (5)
Let the numerator and denominator be 2x and 5x. Now
(2x + 4)/10 = 1/3
X = 3.
Required sum = 2x + 5x = 7x = 21

2. (1)
Required percentage = (750000 - 700000)/700000 * 100 = 7.14%



4. (2)
Number of arrangements = 3! *  6! = 4320

5. (3)
Total score of students = 3 * 90 + 9 * 80 + 4 * 70 + 4 * 60 = 1510
Required average = 1510/20  =  75.5

Solutions (6-10)
Profession Male Female Total
Lawyers 2394 1596 3990
Teachers 630 2520 3150
Architects 1386 924 2310
Engineers 1512 2268 3780
Designers 2184 1176 3360
Doctors 3528 882 4410
Total 11634 9366 21000

6. (1)
Required ratio = (60% of 11) : (20% of 15) = 11 : 5

7. (1)
Required percentage = 20% of 21 = 4.2

8. (2)
Required difference = 11634 – 9366 = 2268

9. (3)
Required percentage =  19/21 * 100 = 90.4%

10. (5)
Required ratio = (1512 + 2184) : 9366 = 88 : 223