Quantitative Aptitude Ques 1576

Question: A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days will all of them together complete the work?

Options:

A) 16 days

B) 15 days

C) 12 days

D) 10 days

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, time taken by (A + B) = 18 days (A + B)’s 1 day’s work $ =\frac{1}{18} $ … (i) Similarly, (B + C)’s 1 day’s work $ =\frac{1}{24} $ … (ii) (A + C)’s 1 day’s work $ =\frac{1}{36} $ … (iii) On adding Eqs. (i), (ii) and (iii), we get 2 (A + B + C)’s 1 day’s work $ =\frac{1}{18}+\frac{1}{24}+\frac{1}{36}=\frac{4+3+2}{72}=\frac{1}{8} $

$ \therefore $ (A + B + C)’s 1 day’s work $ =\frac{1}{16} $

$ \therefore $ A, B and C together will complete the work 16 days.

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