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Question 35 : Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q and R together can complete the work in 30 days then in how many days P alone can do the work?

  1. 52 days
  2. 42 days
  3. 30 days
  4. 50 days

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Explanatory Answer

Let’s consider that P can complete the job in x days.

Work done by P in one day is double the work done by Q in one day, which means P is twice as efficient as Q and takes half the time required by Q to complete the work.
Which means time taken by Q = twice the time taken by P to complete the work.

Time taken by Q to complete the task = 2 * x.

Work done by Q in one day is thrice the work done by R in one day, which means Q is three times as efficient as R and takes one third of the time required by R to complete the work.
Which means time taken by R = thrice the time taken by Q to complete the work.

Time taken by R to complete the task = 3 * 2 * x = 6 * x.

P takes x days to finish the task. So, the fraction of job completed by P in one day is \\frac{1}{x}\\).
Q takes 2x days to finish the task. So, the fraction of job completed by Q in one day is \\frac{1}{2x}\\).
R takes 6x days to finish the task. So, the fraction of job completed by R in one day is \\frac{1}{6x}\\).

If P,Q,R work together, the fraction of work done in one day will be \\frac{1}{x}\\) + \\frac{1}{2x}\\) + \\frac{1}{6x}\\).

It is also given that the three of them can finish the job in 30 days. So if they work together, the fraction of work done in one day will be \\frac{1}{30}\\).

So, \\frac{1}{x}\\) + \\frac{1}{2x}\\) + \\frac{1}{6x}\\) = \\frac{1}{6x}\\)

\\frac{(6+3+1)}{6x}\\) = \\frac{1}{6x}\\)
\\frac{10}{6x}\\) = \\frac{1}{6x}\\)
x = 50 days.

Therefore, P can alone do the work in 50 days.

The question is "Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q and R together can complete the work in 30 days then in how many days P alone can do the work?"

Hence, the answer is 50 days

Choice D is the correct answer

 

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