Question

The ages of A and B are in the ratio $5:3$. After $6$ years, their ages will be in the ratio $7:5$. The sum of their present ages is __________.

• A. $9$ years
• B. $10$ years
• C. $15$ years
• D. $24$ years

Answer 1

Answer: (D)

$24$ years

Let the sum of the ages of $A=5x$ and $B=3x$

Then after $6$ years, their ages are in ratio $7:5$

$\therefore$ $\frac{5x+6}{3x+6}=\frac{7}{5}$

$\therefore$ $25x+30=21x+42$

$4x=12$

$x=3$

Present age of A= $5x=15$

Present age of B=$3x=9$

Sum of present age =$15+9=24$ years