CAT Quantitative Aptitude Questions | CAT Time and Work questions

CAT Questions | Time and work | Work Time

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

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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 and B take 9 days to complete the remaining 60% of the job.
Therefore, in one day A and B can complete – \\frac{60}{9}\\) = \\frac{20}{3}\\) of the job
Since B is twice as fast as A,
B can finish = \\frac{20}{3}\\) * \\frac{2}{3}\\) = \\frac{40}{9}\\) of the job in a day
A can finish = \\frac{20}{3}\\) * \\frac{1}{3}\\) = \\frac{20}{9}\\) of the job in a day
In the first 4 days. A and B would have finished = \\frac{20}{3}\\) * 4 = \\frac{80}{3}\\) of the job
Therefore, C would have finished = 40 % - \\frac{80}{3}\\) = \\frac{40}{3}\\) of the job in 4 days
So, in a day C finishes = \\frac{40}{12}\\) of the job
Thus, clearly B is the fastest among the three workers

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.

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