# Two years back the ratio of ages of Manoj and Sunita is 1 ∶ 2. Three years from now the ratio of their ages will be 3 ∶ 5. Find the present ages of Ma

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Two years back the ratio of ages of Manoj and Sunita is 1 ∶ 2. Three years from now the ratio of their ages will be 3 ∶ 5. Find the present ages of Manoj and Sunita.
1. 22, 12
2. 44, 24
3. 12, 22
4. 32, 18
5. 18, 32

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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.