Quantitative Aptitude

Q1. Shubham was conducting an experiment in which the average of 11 observations came to be 90, while the average of first five observations was 87, and that of the last five was 84. What was the measure of the 6th observation? 

(a) 165

(b) 150 

(c) 145

(d) 135

(e) 125

Q2. A batsman has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs, thereby increasing his average by 5 runs. What is his average after the 13th innings?  

(a) 64

(b) 48

(c) 36

(d) 72

(e) 89

Q3. There was one mess for 30 boarders in a certain hostel. If the number of boarders was increased by 10, the expenses of the mess increased by Rs. 40 per month, while the average expenditure per head diminished by Rs. 2. Find the original monthly expenses.

(a) Rs. 390

(b) Rs. 360

(c) Rs. 410

(d) Rs. 480

(e) Rs. 450

Q4. The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. The mean salary of remaining workers is: 

(a) Rs. 5000

(b) Rs. 7000

(c) Rs. 6000

(d) Rs. 8000

(e) Rs. 9000

Q5. Of the three numbers, the first is twice the second and the second is twice the third. The average of these three numbers is 21. Find the largest number.  

(a) 36

(b) 38

(c) 47

(d) 48

(e) 35

Q6. In a mathematics exam, a student scored 30% marks in the first paper out of a total of 180. How much should he score in the second paper out of a total of 150, if he is to get an overall average of 50%? 

(a) 74%

(b) 76%

(c) 70%

(d) 80%

(e) 75%

Q7. The average marks of a student in 8 subjects is 87. Of these, the highest marks are 2 more than the next in value. If these two subjects are eliminated, the average marks of the remaining subjects is 85. What is highest score? 

(a) 91

(b) 94

(c) 89

(d) 96 

(e) 92

Q8. An officer’s pension on retirement from service is equal to half the average salary during last 36 months of his service. His salary from 1 January, 2014 is Rs. 3800 per month with increment of Rs. 400 on 1 October 2014, October 2015 and 1 October, 2016. If he retires on 1 January, 2017, what pension does he draw? 

(a) Rs. 2100

(b) Rs. 2150

(c) Rs. 2200

(d) Rs. 2250

(e) Rs. 2300

Q9. In a one-day cricket match, Virat, Sehwag, Sachin, Dhoni and Yuvraj scored an average of 39 runs. Dhoni scored 7 more than Yuvraj. Yuvraj scored 9 fewer than Virat. Sehwag scored as many as Dhoni and Yuvraj combined; and Sehwag and Sachin together scored 110 runs between them. How many runs did Sachin score? 

(a) 47

(b) 51

(c) 53

(d) 49

(e) 57

Q10. The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates, who passed the examination was:  

(a) 100

(b) 110

(c) 120

(d) 150

(e) 115

Q11. A painter is paid x rupees for painting every 10 metres of a wall and y rupees for painting every extra metre. During a week, he painted 10 metres on Monday, 13 metres on Tuesday, 12 metres on Wednesday, 11 metres on Thursday and 12 metres on Friday. What is average daily earning in rupees for the five day week?  

(a) x + (8/5)y

(b) (5x + 9y)/5 

(c) 10x + (8/5)y

(d) 5x + 8y 

(e) Cannot be determined

Q12. The average age of a husband and wife was 23 when they were married 5 years ago. The average age of the husband, the wife and a child who was born during the interval, is 20 years now. How old is the child now? 

(a) 9 months 

(b) 1 year 

(c) 3 years 

(d) 4 years 

(e) 2 years

Q13. The average marks of a students in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If the highest score is 92, find the lowest?  

(a) 55

(b) 60

(c) 62

(d) 65

(e) Cannot be determined 

Q14. The average weight of 45 students in a class was calculated as 36 kg. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was 32 kg., but it was calculated as 34 kg. and the weight of another boy in the class was 45 kg. whereas it was calculated as 40 kg. What is the actual average weight of the 45 students in the class? (Rounded off to two-digits after decimal)

(a) 36.07 kg.

(b) 36.16 kg.

(c) 35.84 kg.

(d) Cannot be determined

(e) None of these

Q15. ‘Mr. Hatim’s total annual gross salary, which was Rs. 10 lakhs per year in 2007, has been reduced by 10% in 2008. In 2007 his family expenditure for food items was 40% of the total annual gross salary. The prices of average food items have increased by 5% between 2007 and 2008. Assuming that the family consumed the same amount of food in 2008, the percentage expenditure on food items, calculated on total annual gross salary in 2008, is approximately:   

(a) 43%

(b) 45%

(c) 47%

(d) 49%

(e) 50%

Solutions

S1. Ans.(d)

Sol. 11 × 90 - 5 × 87 - 5 × 84 

= 990- 435 - 420 = 135

S3. Ans.(b)

Sol. Let the original average expenditure be Rs. x

Then, 

40(x - 2) - 30x = 40 

⇒ 10x = 120 ⇒ x = 12 

∴ Original expenditure = 30 × 12 = Rs. 360 

S4. Ans.(c)

Sol. Total salary of 75 workers = Rs. 426000 

Total salary of 25 workers = Rs. 135000 

Total salary of 30 workers = Rs. 171000 

∴ Total salary of remaining 20 workers 

= 426000 - (135000 + 171000) 

= 120000

∴ Mean salary of 20 workers =120000/20 = Rs. 6000. 

S7. Ans.(b)

Sol. Total score of 8 subjects = 87 × 8 = 696 

Total score of 6 subjects = 85 × 6 = 510 

∴ Score of remaining two subjects = 696 - 510 = 186 

Now, let the highest and the next highest score are x and x - 2, then 

(x) + (x - 2) = 186 

⇒ 2x = 188 ⇒ x = 94. 

S9. Ans.(e)

Sol. (Virat + Sehwag + Sachin + David + Yuvraj) 

Make = 39 × 5 = 195 runs

With respect to scoring runs 

Dhoni = Yuvraj + 7 

Yuvraj = Virat - 9 

Sehwag = Dhoni + Yuvraj 

Sehwag + Sachin = 110 

⇒ Virat, Dhoni, Yuvraj, Sehwag and Sachin scored

 = 32, 30, 23, 53 and 57 runs respectively.   

S10. Ans.(a)

Sol. Suppose the number of candidates passed = x 

∴ 39x + 15 (120 - x) = 120 × 35 

⇒ 24x = 120 × 35 - 120 × 15 

= 120 (35 - 15) = 120 × 20 

⇒ x = 100 

S12. Ans.(d)

Sol. Present total age of husband and wife 

= (23 × 2 + 5 × 2) = 56 years 

Present total age of husband, wife and child 

= 20 × 3 = 60 years 

∴ age of child = (60 - 56) = 4 years  

S13. Ans.(b)

Sol. Total marks in 10 papers = 800 

Total marks in 8 papers = 648 

Total of highest and lowest marks = 152 

Lowest marks = 152 - 92 = 60.  

S14. Ans.(a)

Sol. Actual weight of all the students

= 36 × 45 - 34 + 32 - 40 + 45

= 1620 + 3 = 1623kg.

Actual average weight = 1623/45 = 36.07 kg 

 

Quantitative Aptitude

Q1. Three papers were set in an examination and the maximum marks per were in the ratio of 1 : 2 : 2, respectively. If a student obtained 50% in the first paper, 60% in the second, and 65% in the third, what percent did he obtain overall? 

(a) 58.3%

(b) 66.66%

(c) 33.33%

(d) 60%

(e) None of these

Q2. A recipe gives directions to mix 4 pats of substance A with 7 parts of substance B. These substances are to be taken by weight, but by mistake they were taken by volume. Find the error in the percentage of the weight of A in the mixture, if 117 cm3 of the substance A weighs as much as 151 cm3 of the substance B.

(a) 5.05%

(b) 6.00%

(c) 7.05%

(d) 6.02%

(e) None of these

Q3. Tom’s salary is 125% of Tina’s salary. Tito’s salary is 80% of Tina’s salary. The total of all the three salaries is Rs. 61,000. What is Tito’s salary? 

(a) Rs. 16,000

(b) Rs. 16,500

(c) Rs. 15,500

(d) Rs. 15,000 

(e) None of these

Q4. A bag contains 600 pens of brand A and 1200 pens of brand B. If 12% of brand A pens and 25% of brand B pens are removed, then what is the approximately percentage of total pens removed from the bag? 

(a) 37%

(b) 36%

(c) 22%

(d) 18%

(e) None of these

Q5. A person spends 40% of his salary on his educational expenses. He spends 60% of it in purchasing books and one-half of the remaining in purchasing stationery items. If he saves Rs. 160 every month, which is one-fourth of the balance after spending over books and stationery items, what is his monthly salary? 

(a) Rs. 8000

(b) Rs. 4800

(c) Rs. 9600

(d) Data inadequate 

(e) None of these

Q6. A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs. 1000 plus 2.5% commission on all sales exceeding Rs. 4000. If his remuneration as per the new scheme was Rs. 600 more than by the first scheme, what were his sales worth? 

(a) Rs. 11000

(b) Rs. 17000

(c) Rs. 16000

(d) Rs. 12000

(e) None of these

Q7. In an examination it is required to get 296of the total maximum aggregate marks to pass. A student gets 259 marks and is declared failed. The difference of marks obtained by the student and that required to pass is 5%. What are the maximum aggregate marks a student can get?

(a) 690

(b) 780

(c) 740

(d) Cannot be determined 

(e) None of these

Q8. A monthly return railway ticket costs 25% more than a single ticket. A week’s extension can be had for the former by paying 5% of the monthly paid for the monthly ticket (with extensions) is Rs. 84, the price of the single ticket is 

(a) Rs. 64

(b) Rs. 80

(c) Rs 48

(d) Rs 72

(e) None of these

Q9. In three vessels, each of 100 L capacity, mixture of milk and water is failed. The ratio of milk and water are 4 : 1, 2 : 3, 4 : 3 in the respective vessels. If all three vessels are emptied into a single large vessel, then what will be the ratio of water to milk in the resultant mixture?

(a) 43 : 62 

(b) 197 : 214 

(c) 219 : 117 

(d) 179 : 234 

(e) None of these

Q10. In a town, 60% of the adult population is male. a% of the adult males and b% adult females are educated. The total number of educated adult male and uneducated adult females is equal in number to the total number of uneducated adult males and educated adult females. If a and b are both integers, which of the following could be the set of values (a, b)? 

(a) (20, 30)

(b) (20, 10)

(c) (30, 15)

(d) (30, 20)

(e) None of these

Q11. A survey shows that 61%, 46% and 29% of the people watched ‘Airlift’, Neerja’ and ‘Jolly LLB’ respectively. 25% people watched exactly two of the three movies and 3% watched more, what percentage of people watched all the three movies?  

(a) 39%

(b) 11%

(c) 14%

(d) 7%

(e) None of these

Q12. Bennett distribution company, a subsidiary of a major cosmetics manufacture Bavlon, is forecasting the zonal sales for the next year. Zone I with current yearly sales to Rs. 193.8 lakhs is expected to achieve a sales growth of 7.25%; Zone II with current sales of Rs. 79.3 lakhs is expected to grow by 8.2% and Zone III with sales of Rs. 57.5 lakhs is expected to increase sales by 7.15%. What is the Bennett’s expected sales growth for the next year?

(a) 7.46%

(b) 7.53%

(c) 7.88%

(d) 7.41%

(e) None of these

Q13. A man sold a wristwatch for Rs. 2,400 at a loss of twenty five percent. At what rate should he have sold the wristwatch to earn a proflt of twenty five per cent?

(a) Rs. 3,600

(b) Rs. 4,000

(c) Rs. 3,500

(d) Rs. 3,800

(e) Rs. 2,500

Q14. Out of the total production of iron hematite, an ore of iron, 20% of the ore gets wasted. Out of the remaining iron, only 25% is pure iron, if the pure iron obtained in a year from a mine of hematite was 8000 kg then the quantity of hematite mined in the year is:

(a) 400000 kg 

(b) 500000 kg 

(c) 450000 kg 

(d) 600000 kg 

(e) None of these

Q15. The total tractor population in a State is 294000, out of which 150000 are made by Mahindra and Mahindra. Out of every 1000 Mahindra tractors, 98 are red in colour. But only 5.3% of the total tractor population is red. Find percentage of non-Mahindra tractors that are red.

(a) 0.612%

(b) 5.025%

(c) 5.130%

(d) 6.140%

(e) None of these

Quantitative Aptitude

Q1. Half the girls and one-third of the boys of a college reside in the hostel. What fractional part of the student body is hostel dwellers if the total number of girls in the college is 100 and is one-fourth of the total strength?   

(a) Two-fifths 

(b) Five-twelfths 

(c) One-fifth 

(d) Three-eights 

(e) None of these

Q2. The monthly incomes of two persons are in the ratio of 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves Rs. 50 a month, then what are their monthly incomes? 

(a) Rs. 100, Rs. 125

(b) Rs. 200, Rs. 250

(c) Rs. 300, Rs. 375 

(d) Rs. 400, Rs. 500 

(e) None of these

Q3. When a bus started from the first stop, the number of male passengers to the number of female passengers was 3 : 1. At the second stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to female passengers now become 2 :1. What was the total number of passengers in the bus when it started from the first stop?

(a) 64

(b) 48

(c) 54

(d) 72

(e) 80

Q4. X’s income is three-fourths of Y’s income, and X’s expenditure is fourth-fifths of Y’s expenditure.  If X’s income is nine-tenths of Y’s expenditure, find the ratio of X’s savings to Y’s savings.  

(a) 1 : 2

(b) 2 : 1

(c) 1 :4

(d) 2 : 3

(e) None of these

Q5. Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2 : 3 (steps). The ratio of 2nd person’s speed of that of 2nd escalator is 3 : 5 (steps). Find the total number of steps they both have taken together.

(a) 85 

(b) 93

(c) 80

(d) 75

(e) None of these

Q6. A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black pair is double that a brown pair. While preparing the bill, the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50 per cent. The ratio of the number of black and brown pairs of socks in the original order was:  

(a) 4 : 1

(b) 2 : 1

(c) 1 : 4

(d) 1 : 2

(e) None of these

Q7. Two companies A and B quote for a tender. On the tender opening day, A realizes that the two quotes are in the ratio 7 : 4 and hence decreases it price during negotiations to make it Rs. 1 lakh lower than B’s quoted price. B then realises that the final quotes of the two were in the ratio 3 :4. By how much did A decrease its price in order to win the bid?   

(a) Rs. 7 lakhs 

(b) Rs. 4 lakhs 

(c) Rs. 9 lakhs 

(d) Rs. 8 lakhs 

(e) None of these

Q8. A student is studying for a test from 11:00 am to 8:00 pm on weekdays and one-third of that on Saturdays. On Sundays he takes a break from school and goes fishing. For what fractional part of the entire week is the student studying?  

(a) 2/5

(b) 3/7

(c) 2/7

(d) 3/8

(e) None of these

Q9. A sum of Rs. 430 has been distributed among 45 people consisting of men, women and children. The total amounts given to men, women and children are in the ratio 12 : 15 :16. But, the amounts received by each man, woman and child are in the ratio 6 : 5 : 4. Find, what each man, woman and child receives (in Rs.). 

(a) 12, 10, 8

(b) 180, 150, 120

(c) 120, 150,160 

(d) 60, 75, 80

(e) None of these

Q10. The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between  the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers? 

(a) Rs. 750

(b) Rs. 850

(c) Rs. 1000

(d) Rs. 1250 

(e) None of these

Q11. Fresh grapes contain 90 per cent water by weight while dried grapes contain 20 per cent water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes? 

(a) 2 kg 

(b) 2.4 kg 

(c) 2.5 kg 

(d) 3 kg

(e) None of these

Q12. In a certain company, the ratio of the number of managers to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the production-line workers would be 5 to 74. How many managers does the company have?  

(a) 10

(b) 20

(c) 30

(d) 25

(e) None of these

Q13. Mayank, Mirza, Little and Jaspal bought a motorbike for Rs. 60,000. Mayank paid one half of the sum of the amounts paid by the other boys, Mirza paid one third of the sum of the amounts paid by the other boys, Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal has to pay?  

(a) Rs. 15,000

(b) Rs. 13,000

(c) Rs. 17,000

(d) Rs. 16,000

(e) None of these

Q14. I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins is in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one rupee coins.

(a) 90

(b) 85

(c) 100

(d) 105

(e) None of these

Q15. The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond. 

(a) Rs 1.4 lakhs 

(b) Rs 2 lakhs 

(c) Rs. 1 lakhs

(d) Rs. 2.1 lakhs 

(e) None of these

Solutions

S1. Ans.(d)

Sol. Number of girls = 100

∴ Number of boys = 300 

∴ Number of hostel dwellers = 50 + 100 = 150 

⇒ Required ratio = 150 : 400 

=3∶8=3/8 

S2. Ans.(d)

Sol. Let the incomes of the two persons be 4I and 5I respectively

Let the expenditure of the two persons be 7E and 9E respectively.

∴ 4I - 7E = 50 and 5I - 9E = 50 

⇒ 20I - 35E = 250

20I - 36E = 200 

E = 50 and I = 100 

∴ Monthly incomes of the two persons are Rs.400 and Rs. 500 respectively. 

S3. Ans.(a)

Sol. Let, initially, the number of males and females in the bus be 3x and x respectively. 

At the first stop, suppose m males and f females left the bus. 

∴ At the first stop: Number of the males is 3x - m 

And number of females 

 

∴ f = 4, x = 16 

∴ Total number of passengers in the beginning 

= 4x = 64 

For no other value of f any of the other alternatives holds good.  

S4. Ans.(a)

Sol. Let X’s income be 3k then Y’s income is 4k. Let X’s expenditure be 4g then Y’s expenditure is 5g. 

 

S6. Ans.(c)

Sol. Let x pairs brown socks were ordered 

Let p be the price of a brown pair 

∴ 2p is the price of a black pair 

∴ (2p × 4 + px) + 50% of (2p × 4 + px) 

= 2p × x + 4p 

⇒ x = 16 

∴ Required ratio = 1 : 4 

S7. Ans.(b)

Sol. Let the quotes of A and B be 7X and 4X, respectively. 

After decreasing, quotes of A = 4x - 1 

Then, we are given 

 

⇒ X = 1

Then, decreasing by A = 7X - (4X - 1) 

= 3x + 1 = 3 + 1

= Rs. 4 lakhs 

S8. Ans.(c)

Sol. Student studies for 9 hrs from 11 am to 8 pm on Monday to Friday 

Also, be studies 1/3rd of the time on Sunday i.e. 1/3×9=3h 

Total hours, he studied during the week 

= 5 × 9 + 3 = 45 + 3 = 48h 

Total hours, in a week = 24 × 7 = 168 

∴ Required fraction 

=48/168=2/7 

S9. Ans.(a)

Sol. Ratio of personal shares = 6 : 5 : 4 

Ratio of the amounts = 12 : 15 : 16 

Ratio of men, women and children 

=12/6 ∶15/5 ∶16/4 

= 2 : 3 : 4 

Sum of these ratios = (2 + 3 + 4) = 9 

Number of men =((45 × 2)/9)=10 

Number of women =((49 × 3)/9)=15 

And, the number of children = 45 - (10 + 15) = 20 

Now, dividing Rs. 430 in the ratio = 12 : 15 : 16 

Total amount of men’s share 

= Rs. ((430 × 12)/43) 

= Rs. 120 

Total amount of women’s share 

= Rs. ((430 × 15)/43) 

= Rs. 150 

Total amount of children’s share 

= Rs. [430 - (120 + 150)] 

= Rs. 160 

∴ Each man’s share = Rs. (120/10)=Rs.12 

Each woman’s share = Rs. (150/15)= Rs. 10 

Each child’s share = Rs. (160/20) = Rs. 8 

S10. Ans.(d)

Sol. Ratio of the amount collected from the 1st class and the 2nd class passengers = 3 : 50 

∴ Amount collected from the 2nd class passengers 

=50/53×1325 = Rs. 1250.

S12. Ans.(b)

Sol. According to question, 

5x/(72x + 8)=5/74 

⇒ x = 4 

Managers = 5 × 4 = 20 

S13. Ans.(b)

Sol. Mayank paid 1/2 of the sum paid by other three. 
Let the other three paid Rs. x jointly, then Mayank paid x/2

So, x+x/2=60,000 ⇒ x = 40,000. 

Hence, Mayank paid = Rs. 20,000 

Likewise, Mirza and Little paid Rs. 15,000 and Rs. 12,000 respectively. 

Hence, the amount paid by Jaspal is 
Rs. [60,000 - (20,000 + 15,000 + 12,000)] = Rs. 13,000  

S14. Ans.(d)

Sol. Ratio of number of one rupee, fifty paise, and twenty five paise coins = 2.5 : 3:4 

∴ Ratio of value of coins =2.5×1∶3/2 ∶4/4=5∶3∶2 

Let, amount of Rs 1, 50 paise and 25 paise coins be 5x, 3x and 2x respectively. 

So, 5x + 3x + 2x = 210 (given) ⇒ x = 21 

∴ Value of one rupee coins 

= number of one rupee coins = 21 × 5 = 105