The ratio of ages of 2 boys is 3 : 7. After 2 years, the ratio of their ages will become 5 : 9. The ratio of their ages after 10 years will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 13 : 17
The ages are in the ratio 3 : 7, so they can be written as \(3k\) and \(7k\) years. Both boys grow older by the same number of years, and the new ratio fixes \(k\).
After 2 years: \(\displaystyle\frac{3k+2}{7k+2}=\frac{5}{9}\)
\(27k+18=35k+10\)
\(8k=8\), so \(k=1\): the present ages are 3 and 7 years
After 10 years: \(3+10=13\) and \(7+10=17\) years, a ratio of 13 : 17