Given that, total work $=172$ hours.
Let be $x$ regular work hours, then overtime work will be $(172-x)$ hours.
- John gets Rs.$57$ per hour of regular work.
- Then regular income of John $=x\times57$
- John gets Rs.$144$ per hour of overtime work.
- Then overtime income of John $=(172-x)\times114$
His income from overtime hours is $15\%$ of his income from regular hours. Then,
$\Rightarrow (x \times 57) \times \frac{15}{100} = (172-x) \times114$
$\Rightarrow x \times \frac{15}{100} = (172-x) \times 2$
$\Rightarrow \frac{3x}{20} = (344-2x)$
$\Rightarrow 3x = (344-2x) \times 20$
$\Rightarrow 3x = 6880-40x$
$\Rightarrow 43x = 6880$
$\Rightarrow x = 160$
Regular work hours $x = 160$
$\therefore$ Overtime work hours $ = 172-x$
$\qquad =172-160$
$\qquad=12$
Correct answer $:12$