SATHEE: Quantitative Aptitude Ques 971

Quantitative Aptitude Ques 971

Question: B and C together can complete a work in 8 days. A and B together can complete the same work in 12 days and A and C together can complete the same work in 16 days. In how many days can A, B and C together complete the same work?

Options:

A) $ 3\frac{9}{13} $

B) $ 7\frac{5}{13} $

C) $ 7\frac{5}{12} $

D) $ 3\frac{5}{12} $

E) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

(B + C)’s 1 day’s work $ =\frac{1}{8} $ (i) (A + B)‘s1 day’s work $ =\frac{1}{12} $ … (ii) (A + C)’s 1day’s work $ =\frac{1}{16} $ … (iii) On adding Eqs. (i), (ii) and (lii), we get 2 (A + B + C)’s 1 day’s work $ =\frac{1}{8}+\frac{1}{12}+\frac{1}{16}=\frac{6+4+3}{48}=\frac{13}{48} $

$ \Rightarrow $ (A + B + C)’s 1 day’s work $ =\frac{13}{96} $

$ \therefore $ A, B and C together can complete the work in $ =\frac{96}{13}=7\frac{5}{13}days $

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