CAT 2019 Set-2 | Question: 91

Question

John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his income from regular hours. Then, for how many hours did he work overtime _________

Comments

12 hrs.

Answer 1

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 $:12$