This set of Aptitude Questions and Answers (MCQs) focuses on “Word Problems – Set 2”.

1. Out of 40 students of a class 12 are boys. If the average weight of a boy is 50 kg and the average weight of a girl is 20% less than a boy, find the ratio of the total weight of the boys to the total weight of the girls.

a) 1 : 3

b) 2 : 5

c) 3 : 7

d) 4 : 9

View Answer

Explanation: The weight of all the boys of the class = 12 * 50 = 600 kg

The weight of all the girls of the class = (40 – 12) * (50 – 20% of 50) = 28* 50 = 1400 kg

The ratio = 600 : 1400 = 3 : 7

2. The ratio of two numbers is 4 : 5. When 15 is added to the numbers the ratio changes to 11 : 13. Find the numbers.

a) 40, 50

b) 44, 55

c) 36, 45

d) 32, 40

View Answer

Explanation: Let the numbers be in terms of x.

The numbers are 4 : 5 = 4x : 5x

4x + 15 : 5x + 15 = 11 : 13

(4x + 15) / (5x + 15) = 11 / 13

52x + 195 = 55x + 165

3x = 195 – 165 = 30

3x = 30

X = 30 / 3 = 10

4x = 40, 5x = 50

3. The ratio of salaries of two employees is 8 : 11. If the salaries of both combined is 3,30,205 rupees, find the salary of the first employee.

a) 141560 rupees

b) 151460 rupees

c) 145060 rupees

d) 145600 rupees

View Answer

Explanation: Let their salaries be in terms of x.

The salaries combined = 330205

Their salaries = 8 : 11 = 8x : 11x

8x + 11x = 19x = 330205

X = 330205 / 19 = 17695

Salary of the first employee = 8x = 17695 * 8 = 141560 rupees.

4. The salary of a is 65% more than b, Find the ratio of their salaries.

a) 20 : 33

b) 33 : 20

c) 22 : 30

d) 30 : 22

View Answer

Explanation: Let the salary of b be 100.

The salary of a = 65% more than salary of b = 100 + 65% of b = 165

The ratio of their salaries = 165 : 100 = 33 : 20

5. The total number of workers at a factory is 120. There are 5 departments with 20, 30, 30, 20 and 20 employees, respectively. If the number of employees of the first two departments increase by 40% and the employees of the rest of the departments decrease by 60%, find the new ratio of employees.

a) 15 : 20 : 6 : 4 : 4

b) 15 : 22 : 6 : 6 : 4

c) 14 : 21 : 6 : 4 : 4

d) 14 : 21 : 6 : 6 : 4

View Answer

Explanation: The new number of employees for the first department = 20 + 40% of 20 = 20 + 8 = 28

The new number of employees for the second department = 30 + 40% of 30 = 30 + 12 = 42

The new number of employees for the third department = 30 – 60% of 30 = 30 – 18 = 12

The new number of employees for the fourth department = 20 – 60% of 20 = 20 – 12 = 8

The new number of employees for the fifth department = 20 – 20% of 20 = 20 – 12 = 8

The new ratio = 28 : 42 : 12 : 8 : 8 = 14 : 21 : 6 : 4 : 4

6. The ratio of two numbers changes from 14 : 15 to 10 : 11 when 40 is subtracted from it, find the numbers.

a) 126, 135

b) 140, 150

c) 154, 168

d) 168, 182

View Answer

Explanation: Let the numbers be in terms of x.

The number are 15 : 15 = 14x : 15x

14x – 40 : 15x – 40 = 10 : 11

On solving we get x = 10

The numbers = 140, 150

7. The number of employees in a company is 69. If there are 2 departments and the number of employees in first department is 30% more than the other department, find the ratio of employees in the second department to the employees in the first department.

a) 11 : 13

b) 13 : 11

c) 10 : 13

d) 13 : 10

View Answer

Explanation: Let the number of employees in the second department be x.

The total number of employees = 69

The employees in the second department = x

The employees in the first department = x + 30% of x = 1.3x

The total number of employees = x + 1.3x = 2.3x

2.3x = 69

X = 30

The number of employees in the second department = 1.3x = 39

The required ratio = 30 : 39 = 10 : 13

8. There are 221 employees in a company. If there are 2 departments and the employees in the first department are 30% less than the employees in the second department, find the ratio of employees of the first department to the number of employees in the second department.

a) 9 : 7

b) 7 : 9

c) 10 : 7

d) 7 : 10

View Answer

Explanation: Let the number of employees in the second department be x.

The number of employees in the first department = x – 30% of x = 0.7x

The total number of employees = 221

The total number of employees in terms of x = x + 0.7x = 1.7x

1.7x = 221

X = 130

The number of employees in the department second = 130

The number of employees in department first = 221 – 130 = 91

The ratio of employees in the first department to the ratio of employees in the second department = 91 : 130 = 7 : 10

9. The total number of students in a class is 150. If 30% of the student are absent, out of remaining 40% students passed the test. Find the ratio of students absent to the students failed the exam.

a) 7 : 5

b) 6 : 5

c) 5 : 6

d) 5 : 7

View Answer

Explanation: The total number of students = 150

The students absent = 30% of 150 = 45

The number of students present = 150 – 45 = 105

The number of students passed the exam = 105 – 40% of 50 = 63

The required ratio = 45 : 63 = 5 : 7

10. Find the ratio of prime numbers less than 40 to the composite numbers less than 40 except 1.

a) 13 : 6

b) 6 : 13

c) 9 : 5

d) 5 : 9

View Answer

Explanation: Prime numbers less than 40 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Composite numbers less than 40 except 1 = 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21,22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39.

Number of prime numbers = 12

Number of composite numbers = 26

The required ratio = 12 : 26 = 6 : 13

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