CAT Quantitative Aptitude Questions | CAT Time and Work questions

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Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: What fraction of work done by all three and done by the two?

A, B and C complete 40% of the job in 4 days, that means A, B and C complete the entire(100%) job in 10 days.
The rest of the 60% of the job was completed by A and B together, also, this 60% of the job was completed in 13 - 4 = 9 days.

A and B complete 60% of the job in 9 days. This implies that A nd B together would complete the entire(100%) of the job in \\frac{100}{60}) * 9 = 15 days.

We are told that B is twice as fast as A. Or A is half as fast as B. Or in other words A and B together is 1.5 times as efficient as B.
(A + B ) is \\frac{3}{2}\\) times as efficient as B.
(A + B ) take \\frac{2}{3}\\) of the time taken by B to complete the task.
Or, B takes \\frac{3}{2}) times the time taken by (A + B) to complete the task.
Time taken by B = \\frac{3}{2}) × 15 = 22.5 days

We know that B is faster than A, we just need to check if C is faster than B to check the fastest of A, B and C.

A and B complete 60% of the job in 9 days.
A and B can complete 40% of the job in 6 days.
A, B and C complete 40% of the job in 4 days. That means, C works for 4 days to finish the work done by (A + B) in 2 days.
Or in other words, C does \\frac{40%}{3}\\) of work in 4 days.
So C takes 30 days to finish the job.

Hence the fastest of them takes 22.5 days to finish the job.

The question is "How much would the fastest worker take to type the entire set of pages alone?"

Hence, the answer is "22.5 days".

Choice A is the correct answer.