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CAT 2023 Slot 3 — QA Question 16

BasicsEasy

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 & solution

Answer: 36

Solution

Easy

The "make-up" condition compares Gautam's shortfall to Suhani's extra, fixing the ratio of their daily outputs. With the joint 20-day time you get the total work, then the faster worker's solo time is total work divided by his rate.

Let Gautam's and Suhani's daily outputs (efficiencies) be gg and ss units/day.

1

Shortfall = extra. Gautam doing 60%60\% means he is short by 40%40\% of gg; Suhani doing 150%150\% means she adds 50%50\% of ss:

0.4 g=0.5 s⇒ gs=54 ⇒ g=5k, s=4k\begin{aligned} &0.4\,g=0.5\,s\\ &\Rightarrow\ \frac{g}{s}=\frac{5}{4}\ \Rightarrow\ g=5k,\ s=4k \end{aligned}
2

Total work from the 20-day joint completion:

work=20 (g+s)=20 (5k+4k)=180k units\text{work}=20\,(g+s)=20\,(5k+4k)=180k \ \text{units}
3

Faster worker is Gautam (rate 5k>4k5k>4k). His solo time:

180k5k=36 days\frac{180k}{5k}=36 \ \text{days}
Faster worker’s solo time=36 days\text{Faster worker's solo time}=\mathbf{36}\ \text{days}
CAT 2023 Slot 3 QA Q16: Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on — Solution | TheCATExam