Multiple choice

The difference between the present age of a father and that of a son is 32 years. If 14 years ago their ages were in the ratio of 5 : 3. Find the ratio between their ages after 6 years.

  1. $17:25$
  2. $25:17$
  3. $15:23$
  4. $23:15$
  5. $5:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let current ages be father = F, son = S. F - S = 32. 14 years ago: (F-14)/(S-14) = 5/3. Cross-multiplying: 3F - 42 = 5S - 70, so 3F - 5S = -28. Substituting F = S + 32: 3(S+32) - 5S = -28, giving S = 62. So F = 94. After 6 years: father = 100, son = 68. Ratio = 100:68 = 25:17.