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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