CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 9 Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

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Video Explanation

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Explanatory Answer

We are looking for a number which can be a multiple of 2 and 3 . It is 6 .
Let us imagine:
In one day, the part of work done by
Mohit \(=6 k ;\) Sam \(=3 k ;\) Ayna \(=2 k\).
Then,
\(\left.\begin{array}{l}\text { Day } 1 \Rightarrow \text { Sam \& Mohit }=9 k \\ \text { Day } 2 \Rightarrow \text { Sam \& Ayna }=5 k \\ \text { Day } 3 \Rightarrow \text { Mohit \& Ayna }=8 k\end{array}\right] \quad[22 k\) work done in 1 cycle \(]\)
In 2 cycles, (i.e., in 6 days) 44k work would be done. And the cycle repeats.
Then,
Day 7 ⇒ Sam & Mohit = 9k
Day 8 ⇒ Sam & Ayna = 5k
Day 9 ⇒ Mohit & Ayna = 2k
[Remaining 2k work to be done]
So, technically Sam worked for 6 days. [i.e., first 2 days in each cycle]
Then, the part of work done by Sam = 18k
Fraction of total work done by Sam \(=\frac{18 k}{60 k}=\frac{3}{10}\)

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The question is "Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is"

Hence, the answer is '3/10'

Choice B is the correct answer.

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