Question

The ratio of the ages of two boys is $5:6.$ After $2$ years, the ratio of their ages will be $7:8.$ The ratio of the their ages after $10$ years will be

• A. $15:16$
• B. $17:18$
• C. $11:12$
• D. $22:24$

Answer 1

The correct option is A $15:16$

Let the ages of the two boys be 5x and 6x.
Given, $\frac{5x+2}{6x+2}=\frac{7}{8}\Rightarrow 40x+16=42x+14$
$\Rightarrow 2x=2\Rightarrow x=1$
$\therefore$ Required ratio $=(5x+10):(6x+10)=(5\times 1+10):(6\times 1+10)=15:16$