Multiple choice

Ratio of the present age of a mother to that of the daughter is 7 ∶ 1. After 5 years the ratio will become 4 ∶ 1. What is the difference (in years) in their present ages?

  1. 30

  2. 31

  3. 29

  4. 28
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A Correct answer
Explanation

Let present ages be 7x and x. After 5 years: (7x+5)/(x+5) = 4/1. Solving: 7x+5 = 4x+20, so 3x = 15, giving x = 5. Present ages are 35 and 5, so difference = 30 years. Alternatively, using ratio properties: the difference of 6 parts (7-1) remains constant, so 6 parts = 30, meaning 1 part = 5.

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