Correct Answer - Option 3 : 12, 22
Given:
Two years back the ratio of ages of Manoj and Sunita = 1 ∶ 2
Three years from now the ratio of their ages will be 3 ∶ 5
Calculations:
Let the present ages of Manoj and Sunita be M and S respectively.
Two years back the ratio of ages of Manoj and Sunita = 1 ∶ 2
⇒ (M – 2)/(S – 2) = 1/2
⇒ 2M – S = 2 ----(1)
Three years from now the ratio of their ages will be 3 ∶ 5
⇒ (M + 3)/(S + 3) = 3/5
⇒ 5M – 3S = -6 ----(2)
Multiply equation (1) with 3
⇒ 3(2M – S) = 2 × 3
⇒ 6M – 3S = 6 ----(3)
Substrate equation (2) from equation (3)
⇒ 6M – 3S – (5M – 3S) = 6 – (-6)
⇒ M = 12
Put the value of M in equation (1)
⇒ 2 × 12 – S = 2
⇒ S = 22
∴ Age of Manoj and Sunita is 12 and 22 respectively.
