Test: Problem on Ages - UPSC MCQ

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.

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.

Let the mother's present age be x years.

 2(2x + 40) = 5(x + 8)

 x = 40.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.