Multiple choice

Ratio between age of A and B four year ago was (9: 10) and ratio between both age four year hence will be (13: 14). What was the sum of both ages 10 year ago?

  1. 50 years

  2. 48 years

  3. 32 years

  4. 28 years

  5. None of these
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E Correct answer
Explanation

Let A and B be present ages. Four years ago: (A-4)/(B-4) = 9/10, giving 10A - 40 = 9B - 36, so 10A = 9B + 4. Four years hence: (A+4)/(B+4) = 13/14, giving 14A + 56 = 13B + 52, so 14A - 13B = -4. Solving: A = 22 years, B = 24 years. Sum 10 years ago = (22-10) + (24-10) = 26 years, which matches 'None of these'.

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