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Test: Problem on Ages - UPSC MCQ


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15 Questions MCQ Test CSAT Preparation - Test: Problem on Ages

Test: Problem on Ages for UPSC 2024 is part of CSAT Preparation preparation. The Test: Problem on Ages questions and answers have been prepared according to the UPSC exam syllabus.The Test: Problem on Ages MCQs are made for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Problem on Ages below.
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Test: Problem on Ages - Question 1

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).

Detailed Solution for Test: Problem on Ages - Question 1

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Test: Problem on Ages - Question 2

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?

Detailed Solution for Test: Problem on Ages - Question 2

Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.

Test: Problem on Ages - Question 3

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?

Detailed Solution for Test: Problem on Ages - Question 3

Let the mother's present age be x years.


 2(2x + 40) = 5(x + 8)

 x = 40.

Test: Problem on Ages - Question 4

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?

Detailed Solution for Test: Problem on Ages - Question 4

Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.

Test: Problem on Ages - Question 5

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:

Detailed Solution for Test: Problem on Ages - Question 5

Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

Test: Problem on Ages - Question 6

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

Detailed Solution for Test: Problem on Ages - Question 6

Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.

⇒ 9x - 63 = 7x
⇒ 2x = 63
⇒ x = 31.5
Hence, Sachin's age = (x - 7) = 24.5 years.

Test: Problem on Ages - Question 7

At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?

Detailed Solution for Test: Problem on Ages - Question 7

Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
⇒ 4x + 6 = 26
⇒ 4x = 20
⇒ x = 5.
∴ Deepak's age = 3x = 15 years.

Test: Problem on Ages - Question 8

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

Detailed Solution for Test: Problem on Ages - Question 8

Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14.
∴ Son's age after 6 years = (x + 6) = 20 years.

Test: Problem on Ages - Question 9

Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

Detailed Solution for Test: Problem on Ages - Question 9

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

⇒ 10(6x + 10) = 11(5x + 10)
⇒ 5x = 10
⇒ x = 2.
∴ Sagar's present age = (5x + 6) = 16 years.

Test: Problem on Ages - Question 10

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

Detailed Solution for Test: Problem on Ages - Question 10

Let the son's present age be x years. Then, man's present age = (x + 24) years.
⇒ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
⇒ x = 22.

Test: Problem on Ages - Question 11

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

Detailed Solution for Test: Problem on Ages - Question 11

Let the present ages of Sameer and Anand be 5x years and 4x years respectively.

⇒ 9(5x + 3) = 11(4x + 3)

⇒ 45x + 27 = 44x + 33

⇒ 45x - 44x = 33 - 27

⇒ x = 6.

∴ Anand's present age = 4x = 24 years.

Test: Problem on Ages - Question 12

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Detailed Solution for Test: Problem on Ages - Question 12

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
⇒ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
∴ Hence, B's age = 2x = 10 years.

Test: Problem on Ages - Question 13

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

Detailed Solution for Test: Problem on Ages - Question 13

Let the son's present age be x years. Then, (38 - x) = x

⇒ 2x = 38.

⇒ x = 19.

∴ Son's age 5 years back (19 - 5) = 14 years.

Test: Problem on Ages - Question 14

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

Detailed Solution for Test: Problem on Ages - Question 14

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
∴ Age of the youngest child = x = 4 years.

Test: Problem on Ages - Question 15

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

Detailed Solution for Test: Problem on Ages - Question 15

Let Ronit's present age be x years. Then, father's present age = (x + 3x) years = 4x years.


⇒ 8x + 16 = 5x + 40

⇒ 3x = 24

​​​​​​​⇒ x = 8.

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