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?

- 22.5 days
- 45 days
- 30 days
- 20 days

22.5 days

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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?"**

Choice A is the correct answer.

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