Question:
Tick (✓) the correct answer:
The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is
(a) 20 years
(b) 28 years
(c) 15 years
(d) 21 years
Solution:
(b) 28 years
Let $\mathrm{x}$ be the common multiple of the ages of $\mathrm{A}$ and $\mathrm{B}$.
Then. the age $s$ of $\mathrm{A}$ and $\mathrm{B}$ would be $5 \mathrm{x}$ and $7 \mathrm{x}$, respectively.
$\therefore \frac{5 x+4}{7 x+4}=\frac{3}{4}$
$\Rightarrow 4(5 x+4)=3(7 x+4)$
$\Rightarrow 20 x+16=21 x+12$
$\Rightarrow 16-12=21 x-20 x$
$\Rightarrow 4=x$
$\Rightarrow x=4$
$\therefore$ Age of $B=7(x)=7 \times 4$
$=28$ years