Multiple choice

7 years ago the ratio of age of Amit and Sachin was (11 : 5). From 2 years hence this ratio will become (7 : 4). Find the sum of their ages after 5 years.

  1. 66 years

  2. 72 years

  3. 60 years

  4. 86 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let current ages be A (Amit) and S (Sachin). 7 years ago: (A-7) : (S-7) = 11 : 5, so 5(A-7) = 11(S-7), giving 5A - 35 = 11S - 77, or 5A - 11S = -42. 2 years hence: (A+2) : (S+2) = 7 : 4, so 4(A+2) = 7(S+2), giving 4A + 8 = 7S + 14, or 4A - 7S = 6. Solving: from first, A = (11S - 42)/5. Substituting: 4(11S - 42)/5 - 7S = 6. Multiply by 5: 44S - 168 - 35S = 30, so 9S = 198, S = 22. Then A = (242 - 42)/5 = 40. After 5 years: A = 45, S = 27. Sum = 45 + 27 = 72. Option B is correct.

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