Question

The ratio of the present ages of two brothers is $4:5$ . After $10$ years, the ratio of their ages would be $6:7$ . Find the age of the elder brother after $15$ years.

• A. $35$ years
• B. $40$ years
• C. $50$ years
• D. $25$ years

Answer 1

The correct option is B $40$ years

let present ages be $x$ and $y$

$\frac{x}{y}=\frac{4}{5}$ $\Rightarrow$ $5x=4y\Rightarrow x=4(y-x)$ .....(i)

after 10 years $x$ will be $x+10$

and $y$ will be $y+10$

$\frac{x+10}{y+10}=\frac{6}{7}$

$7x+70=6y+60$

$x+10=6(y-x)$

$x+10=6\left(x/4\right)$ (from (i))

$\frac{2x}{4}=10$

$x=20$

$\Rightarrow y=\frac{5x}{4}=25$

age of elder brother after 15 years $=25+15$

$=40$ years.