Problems on Ages Practice Test 1 with solutions

Let one year ago the ages of Yamini and Gamini were 6x and 7x years respectively; then
$\frac{6\mathit{x}+5}{7\mathit{x}+5}$ = $\frac{7}{8}$
⇒ 48x + 40 = 49x + 35
∴ x = 5
Hence, present age of Gamini = 7x +1 = 7 × 5 + 1 = 36 years

(OR)

Let the age of Yamini one year ago be $6\mathit{x}$.
Let the age of Gamini one year ago be $7\mathit{x}$.
4 years hence:
$\left(\left(6\mathit{x}+1\right)+4\right)∕\left(\left(7\mathit{x}+1\right)+4\right)=7∕8$
$\left(6\mathit{x}+5\right)∕\left(7\mathit{x}+5\right)=7∕8$
$8\left(6\mathit{x}+5\right)=7\left(7\mathit{x}+5\right)$
$48\mathit{x}+40=49\mathit{x}+35$
$\mathit{x}=5$
Gamini age $=7\mathit{x}+1$
$=7\left(5\right)+1$
$=36$ years.
Hence, Gamini's age is 36 years.