This set of Aptitude Questions and Answers (MCQs) focuses on “Word Problems”.

1. The students of science commerce and arts are in a ratio 2 : 3 : 2. If the pass percentage of commerce is 40% and the total students passing in commerce are 12, find the total students combined of all three sections.

a) 21

b) 30

c) 57

d) 70

View Answer

Explanation: The total students of commerce :

Passing students of commerce = 40% = 12 students

100% of the students of commerce section = 12 / 40 * 100 = 12 * 2.5 = 30

The ratio of students in science to commerce to arts = 2 : 3 : 2

Here 3 parts of the total = 30

Total parts = 2 + 3 + 2 = 7

3 parts = 30

7 parts = 30 / 3 * 7 = 70

The total number of students = 70

2. There are a total of 1236 students in a school. If the boy to girl ratio is 1 : 2, find the difference between number of girls and boys.

a) 412

b) 824

c) 241

d) 214

View Answer

Explanation: The number of girls = 1236 / 3 * 2 = 412 * 2 = 824

Number of boys = 1236 / 3 * 1 = 412

Difference = 824 – 412 = 412

3. The total number of employees in a company is 777. If there are 4 departments with employee ratio 3 : 3 : 6 : 9, find the employees in the department with maximum number of employees.

a) 111

b) 222

c) 333

d) 250

View Answer

Explanation: The total number of employees = 777

The employees in the department with the maximum number of employees will be in terms of the 9.

The number of employees with the highest employed department = 777 / 21 * 9 = 333

4. Gold and platinum are mixed in a ratio 8 : 9 to make a ring. Find the ratio of their price in the ring if the price of platinum is 0.7 times the price of gold.

a) 4 : 3

b) 80 : 63

c) 81 : 56

d) 88 : 78

View Answer

Explanation: Let the price of gold per unit be x.

The price of gold in the ring = x * 8 = 8x

The price of platinum per unit = 0.7 times the price of gold = 0.7x

The price of platinum in the ring = 0.7x * 9 = 6.3x

The ratio of price of gold to platinum in the ring = 8x : 6.3x = 80 : 63

5. The price of two litres of milk is equal to the price of 12 litres of water. Find the ratio of price of water to milk in a mixture of 3 litres of water and 11 litres of milk.

a) 11 : 2

b) 2 : 11

c) 1 : 22

d) 22 : 1

View Answer

Explanation: Let the price of 1 litre of milk be x.

The price of 2 litres of milk = 2 * x = 2x

The price of 1 litre of water = 2x / 12 = x / 6

The price of milk in the mixture = x * 11 = 11x

The price of water in the mixture = x * 3 / 6 = x / 2 = 0.5x

The ratio of price of water to milk in the mixture = 0.5x : 11x = 1 : 22

6. The total number of fishes in a batch are 230. If the ratio of 5 categories of fishes is 5 : 5 : 4 : 3 : 6. Find the greatest difference between any two categories of fishes.

a) 230

b) 210

c) 10

d) 30

View Answer

Explanation: Let the ratio be in terms of x.

The ratio 5 : 5 : 4 : 3 : 6 = 5x : 5x : 4x : 3x : 6x

The maximum difference can be 6x – 3x = 3x

Now5x + 5x + 4x + 3x + 6x = 230, 23x = 230

3x = 230 / 23 * 3 = 30

7. There are 4 breeds of dogs available at a pet store. If the ratio of those dogs available is 3 : 7 : 1 : 23, find the total number of dogs available. It is known that the minimum number of dogs of any breed available is 19.

a) 464

b) 446

c) 646

d) 664

View Answer

Explanation: The minimum number of dogs of any breed is 19.

Let the number of dogs be in terms of x.

The number of dogs will be 3x, 7x, x and 23x.

X = the minimum number of dogs available of any breed = 19

X = 19, 3x = 57, 7x = 133 and 23x = 437

The total number of dogs available = 437 + 133 + 57 + 19 = 646

8. The ratio of ages of a couple is 7 : 8. After 5 years their ages will be in a ratio 8 : 9. Find their current ages.

a) 21, 24

b) 28, 32

c) 35, 40

d) 42, 49

View Answer

Explanation: Let their ages now be in terms of x.

Their ages now = 7 : 8 = 7x : 8x

Their ages after 5 years = 7x + 5, 8x + 5

7x + 5 : 8x + 5 = 8 : 9

7x + 5 / 8x + 5 = 8 / 9

63x + 45 = 64x + 40

64x – 63x = 45 – 40 = 5

X = 5

Their current ages = 7x, 8x = 35, 40

9. There are 120 colours in a box out of which 55 are hot colours and the rest are cool colours. Find the ratio of 1 / 10^{th} of hot colours and 1 / 5^{th} of the cool colours.

a) 11 : 13

b) 11 : 18

c) 11 : 22

d) 11 : 26

View Answer

Explanation: The total number of colours = 120

Hot colours = 55 and cool colours = 120 – 55 = 65

The ratio of 1 / 10

^{th}of the hot colours to 1 / 5

^{th}of the cool colours = 55 / 10 : 65 / 5 = 5.5 : 13

5.5 : 13 = 11 : 26

10. Out of 110 students 20 failed the exam. Out of the remaining 20% passed the exam with distinction. Find the ratio of the students who passed the exam to the students who passed the exam without distinction.

a) 4 : 5

b) 5 : 4

c) 3 : 4

d) 4 : 3

View Answer

Explanation: The total number of students who passed the exam = 110 – 20 = 90 students

The number of students passing the exam with distinction = 20% of 90 = 18 students

The remaining students = 90 – 18 = 72 students

The ratio required = 90 : 72 = 5 : 4

11. Work done by 5 men in a day is equal to the work done by 12 children in a day. Find the ratio of their per person efficiencies.

a) 25 : 144

b) 12 : 5

c) 5 : 12

d) 144 : 25

View Answer

Explanation: The efficiency of 5 men = (lcm of 5 and 12) / 5 = 12

The efficiency of 1 man = 12 / 5

The efficiency of 12 boys = (lcm of 5 and 12) / 12 = 5

The efficiency of 1 boy = 5 / 12

Their ratios = 12 / 5 : 5 / 12 = 144 : 25

12. The ratio of ages of 2 sisters is 4 : 5. After 7 years the ratio of their ages will be 5 : 6. Find their current ages.

a) 35, 42

b) 28, 35

c) 21, 28

d) 14, 21

View Answer

Explanation: Let the present ages the sisters be in terms of x.

Their current ages = 4x, 5x

Their ages after 7 years = 4x + 7 : 5x + 7 = 5 : 6

24x + 42 = 25x + 35

25x – 24x = 42 – 35 = 7

X = 7

Their current ages = 4x, 5x = 28, 35

13. Two numbers are in a ratio 7 : 13. If 12 is added to the numbers the ratio turns to 61 : 103, find the numbers when 109 is added to them.

a) 79 : 200

b) 78 : 101

c) 79 : 100

d) 78 : 100

View Answer

Explanation: Let the numbers be in terms of x.

The initial numbers are 7x, 13x.

7x + 12 : 13x + 12 = 61 : 103

On solving we get x = 7

The terms will be 49, 91

When 109 is added to the terms the numbers will be 158, 200.

The ratio of the numbers will be 79 : 100.

14. Out of 3 members in a family 2 are aged 20 years and 44 years. The third member is twice as old as the youngest person. Find the ratio of the family when their ages are arranged in descending order.

a) 22 : 10 : 5

b) 11 : 10 : 10

c) 11 : 20 : 5

d) 11 : 10 : 5

View Answer

Explanation: The youngest member is 20 years

The third member is twice as old as the youngest = 20 * 2 = 40 years

The ages in descending order = 44, 40, 20 years

Their ratio = 11 : 10 : 5

15. The total age of a family is 120 years if the ages of the only 24 members of the family are in a ratio 1 : 2 : 4 : 5, find the ratio of the ages of the family members after 8 years.

a) 1 : 2 : 4 : 5

b) 9 : 14 : 24 : 29

c) 8 : 15 : 23 : 27

d) 10 : 16 : 26 : 31

View Answer

Explanation: Let their ages be in terms of x.

X + 2x + 4x + 5x = 120 years

12x = 120 years

X = 10 years

X = 10 years, 2x = 20 years, 4x = 40 years, 5x = 50 years

After 8 years their ages will be 18, 28, 48 and 58 years.

The ratio of their ages will be 9 : 14 : 24 : 29.

16. There are 30 employees in an office. If the average age of the first 15 employees is half the average age of the rest of the employees. Find the ratio of the average ages of the employees of the two groups after 6 years. The total age of the employees is 1125 years.

a) 30 : 57

b) 30 : 53

c) 31 : 56

d) 31 : 57

View Answer

Explanation: The total age of the first group is half the total age of the second group.

15x + 15x * 2 = 45x = 1125

X = 25 years

The average age of the first group = 25 years

The average age of the second group = 25 * 2 = 50 years

After 6 years the average age of the first group = 25 + 6 = 31 years

After 6 years the average age of the second group = 50 + 6 = 56 years

The required ratio = 31 : 56

17. The total age of 5 people is 200. If their ages are in a ratio 1 : 2 : 3 : 4 : 5, find the age of the youngest person in months.

a) 120 months

b) 140 months

c) 160 months

d) 180 months

View Answer

Explanation: The total of the age in months = 200 * 12 = 2400 months

The age of the youngest person in months = 2400 / 15 * 1 = 160 months

18. The ratio of ages of 2 people are in a ratio 2 : 5. After 9 years the ratio of their ages will be 1 : 2. Find their current ages.

a) 27, 45 years

b) 18, 45 years

c) 27, 36 years

d) 18, 36 years

View Answer

Explanation: Let their current ages be in terms of x.

Their current ages = 2x, 5x

After 9 years their ages will be 2x + 9 : 5x + 9 = 1 : 2

4x + 18 = 5x + 9

5x – 4x = 18 – 9

X = 9

Their current ages = 2x, 5x = 18, 45 years.

19. Three numbers are in a ratio 7 : 8 : 9. If the difference between the largest and the smallest number is 8, find the middle number.

a) 8

b) 16

c) 20

d) 24

View Answer

Explanation: Let the numbers be in terms of x.

The numbers are 7x, 8x and 9x.

9x – 7x = 2x = 8

2x = 8

X = 8 / 2 = 4

The middle number = 8x = 8 * 4 = 24

20. The total of 3 numbers is 121. If the numbers are in a ratio 3 : 4 : 4, find the ratio of the numbers when 11 is added to each number.

a) 2 : 3 : 4

b) 3 : 4 : 5

c) 4 : 5 : 5

d) 5 : 6 : 7

View Answer

Explanation: Let the numbers be in terms of x.

The numbers are 3x, 4x, 4x.

The total = 11x = 121

X = 121 / 11 = 11

The numbers = 3x, 4x, 4x = 33, 44, 44

The ratio when 11 is added to each term = 33 + 11 : 44 + 11 : 44 + 11 = 44 : 55 : 55 = 4 : 5 : 5

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