Time and Work with Work Rates

CAT 2023 Slot 3 · QA · Easy · Arithmetic

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Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

Answer

36

Explanation

Let GG and SS be the daily work done by Gautam and Suhani.

Given: 0.6G+1.5S=G+S  ⟹  0.5S=0.4G  ⟹  GS=540.6 G + 1.5 S = G + S \implies 0.5 S = 0.4 G \implies \frac{G}{S} = \frac{5}{4}

Thus, Gautam is the faster worker.

Together, they finish the job in 20 days: Total Work=20(G+S)=20(G+45G)=20×95G=36G\text{Total Work} = 20(G + S) = 20\left(G + \frac{4}{5}G\right) = 20 \times \frac{9}{5}G = 36 G

So Gautam working alone takes 3636 days.

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