CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and Work: Typing pages. Some details about a completed task are given and we need to determine who is efficient among them?

Question 22: A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?

1. 22.5 days
2. 45 days
3. 30 days
4. 20 days

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 \\farc{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 \\farc{3}{2}) times the time taken by (A + B) to complete the task.
Time taken by B = \\farc{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 \\farc{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.