Question

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

• A. \( 15:16 \)
• B. \( 5:17 \)
• C. \( 17:18 \)
• D. \( 13:17 \)

Hint:

\textbf{Age-Related Problems.} When dealing with age ratio problems, it's often helpful to represent the current ages using a common variable and then set up equations based on the information given about their ages at a future or past time.

Answer 1

The Correct Option is D

Let the present ages of the two boys be \(3x\) and \(7x\) years. After 2 years, their ages will be \(3x + 2\) and \(7x + 2\) years respectively. According to the problem, the ratio of their ages after 2 years will be 5:9. Therefore, we can write the equation: $$ \frac{3x + 2}{7x + 2} = \frac{5}{9} $$ Cross-multiplying, we get: $$ 9(3x + 2) = 5(7x + 2) $$ $$ 27x + 18 = 35x + 10 $$ $$ 18 - 10 = 35x - 27x $$ $$ 8 = 8x $$ $$ x = 1 $$ So, the present ages of the two boys are \(3 \times 1 = 3\) years and \(7 \times 1 = 7\) years. We need to find the ratio of their ages after 10 years. After 10 years, their ages will be \(3 + 10 = 13\) years and \(7 + 10 = 17\) years respectively. The ratio of their ages after 10 years will be \(13:17\). Therefore, the correct option is (D)