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?

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12 — Easy Let regular hours be $x$ and overtime hours be $y$. Write the two facts — total hours, and overtime income $=15\%$ of regular income — as equations and solve. 1 Income condition. Regular income $=57x$, overtime income $=114y$, with overtime $=15\%$ of regular. $$\begin{aligned} &114y = 0.15	imes 57x\ &\Rightarrow\ 114y = 8.55x\ &\Rightarrow\ y = 0.075x \end{aligned}$$ 2 Total-hours condition. $x+y=172$. Substitute step 1. $$\begin{aligned} &x + 0.075x = 172\ &\Rightarrow\ 1.075x = 172\

CAT 2019 Slot 2 — QA Question 34

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