CAT 2024 - Slot 3 Quant Question 5
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CAT 2024 Slot 3 - Quant
We are given that Sam completes a piece of work in 20 days.
We are also given that Mohit is twice as fast, so he should take only 10 days.
Mohit is thrice as fast as Ayna, so he would take 30 days.
Let's take the total work to be 60 units; this would give the work done per day for Mohit, Sam, and Ayna to be 6, 3 and 2, respectively.
On the first day Sam and Mohit work: doing 9 units
On the second day Sam and Ayan work: doing 5 units
On the third day, Mohit and Ayan work: doing 8 units
Essentially doing 22 units in a 3 days cycle.
After two such cycles, there will be 60 – 44 = 16 units of work left
On day 7, Sam and Mohit would work 9 units, leaving 7 units
On day 8, Sam and Ayan would work 5 units, leaving 2 units
And on day 9, Ayan and Mohit would complete the remaining work.
So Sam worked for a total of 2 + 2 + 2 = 6 days and on each day he did 3 units of work, completing 18 units of work.
The ratio of work done by Sam would be 18/60 = 3/10