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Regular vs overtime work hours

CAT 2019 Slot 2 · Quantitative Ability · Medium · Work & time

This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Work & time. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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?

[TITA]

Answer

12

Explanation

Let RR be the regular hours and TT be the overtime hours. R+T=172R + T = 172

Regular income =57R= 57 R, Overtime income =114T= 114 T. Given: 114T=0.15×57R114 T = 0.15 \times 57 R 114T=8.55R  ⟹  T=0.075R114 T = 8.55 R \implies T = 0.075 R

Substitute T=0.075RT = 0.075 R into total hours equation: R+0.075R=172  ⟹  1.075R=172  ⟹  R=160R + 0.075 R = 172 \implies 1.075 R = 172 \implies R = 160 T=172−160=12 hoursT = 172 - 160 = 12\text{ hours}

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