DRDO Multi tasking staff Model paper 9

Let the present age of father, mother and son be F, M and S years respectively.
⇒ (F + 10) ∶ (S + 10) = 13 ∶ 6
⇒ 6F + 60 = 13S + 130
⇒ 6F – 13S = 70
Then,
⇒ (M – 5) ∶ (S – 5) = 8 ∶ 3
⇒ 3M – 15 = 8S – 40
⇒ 8S – 3M = 25
Given,
⇒ (F – 25) – (M – 25) = 10
⇒ F – M = 10
⇒ 6(10 + M) – 13S = 70
⇒ 6M – 13S = 10
Solving,
⇒ S = 20 years
⇒ M = 45 years
⇒ F = 45 + 10 = 55 years
Required sum of ages = 55 + 45 + 20 = 120 years.