Multiple choice

Three years ago ratio of age of Ankita and Rohan was 7 : 4 which becomes 5 : 3 one years hence. Find the sum of this present ages.

  1. 82 years

  2. 94 years

  3. 98 years

  4. 102 years

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

Three years ago, Ankita:Rohan = 7:4. So (A-3)/(R-3) = 7/4, giving 4(A-3) = 7(R-3), so 4A - 12 = 7R - 21, therefore 4A - 7R = -9. One year hence (meaning one year from now), Ankita:Rohan = 5:3. So (A+1)/(R+1) = 5/3, giving 3(A+1) = 5(R+1), so 3A + 3 = 5R + 5, therefore 3A - 5R = 2. Solving: From second eq, 3A = 5R + 2, so A = (5R + 2)/3. Substituting in first: 4(5R + 2)/3 - 7R = -9, so (20R + 8)/3 - 7R = -9, so 20R + 8 - 21R = -27, so -R + 8 = -27, therefore R = 35. Then A = (5×35 + 2)/3 = 177/3 = 59. Sum = 59 + 35 = 94 years. This matches option B.

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