Quantitative Aptitude Ques 2345

Question: A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can finish the work?

Options:

A) 10

B) 20

C) 30

D) 60

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ (P+Q)’s $ 1 day’s work $ =\frac{1}{12} $ ….(i) $ (Q+R)’s $ 1 day’s work $ =\frac{1}{15} $ ….(ii) $ (R+P)’s $ 1 day’s work $ =\frac{1}{20} $ ….(iii) On adding Eqs. (i), (ii) and (iii), we get $ 2(P+Q+R)’s $ 1 day’s work $ =\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{5+4+3}{60}=\frac{12}{60}=\frac{1}{5} $

$ \therefore $ $ (P+Q+R)’s $ 1 day’s work $ =\frac{1}{10} $ ….(iv)

$ \therefore $ P’s 1 day s work $ =\frac{1}{10}-\frac{1}{15}=\frac{3-2}{30}=\frac{1}{30} $ So, P alone will complete the work in 30 days.

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