The ratio of the present ages of a man and his wife is 5 : 8. After 10 years, the ratio of the man and his wife will be 2 : 3. What will be the ratio of their ages after 20 years?

  1. 9 : 10
  2. 3 : 5
  3. 4 : 5
  4. 7 : 10
  5. 3 : 7

Answer (Detailed Solution Below)

Option 4 : 7 : 10
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Detailed Solution

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Let the ages of the man and his wife be 5x and 8x respectively.

After ten years,

ratio of the man and his wife will be 2 : 3;

⇒ (5x + 10) / (8x + 10) = 2 : 3

Hence, x = 10

The ages of the man and his wife are 50 and 80 respectively.

∴ The ratio of their ages after 20 years is 70 : 100 = 7 : 10

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