CAT 2023 Question Paper | Quant Slot 3

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 16 : 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

Video Explanation

Explanatory Answer

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.
This means 40% of Gautam's work in a day = 50% of Suhani's work in a day
40% of Gautam's capacity' = 50% of Suhani's capacity
Gautam is 1.25 as efficient as Suhani.
Let us say Suhani can finish the 1 piece of work in x days. Then, Gautam can finish 1.25 pieces of work in x days.
So, if they work together, they for x days, they can finish 2.25 pieces of work.
So, to finish one piece of work they need \( \frac { x } { 2.25 } \) days.
\( \frac { x } { 2.25 } = 20 \)
x = 45 days.
Since Gautam is 1.25 times faster than Sahani, he takes \( \frac { 45 } { 1.25 } = 36 \)days.
So, the faster one takes 36 days to finish the job.

The question is " 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 "

The answer is '36'