Quantitative Aptitude Ques 1057

Question: A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In how many days, all the three together can do the work?

Options:

A) 80 days

B) 100 days

C) 60 days

D) 150 days

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] $ (A+B)’s $ 1 day’s work $ =\frac{1}{72} $ $ (B,+C)’s $ 1 day’s work $ =\frac{1}{120} $ $ (A+C)’s $ 1 day’s work $ =\frac{1}{90} $ $ 2,(A+B+C)=\frac{1}{72}+\frac{1}{120}+\frac{1}{90} $ $ =\frac{5+3+4}{360}=\frac{1}{30} $ $ A+B+C=\frac{1}{30\times 2}=60,days $ Alternate Method Time taken by $ (A+B+C) $ to complete the total work $ =\frac{2\times (LCMof72,,120and90)}{\frac{LCM}{72}+\frac{LCM}{120}+\frac{LCM}{90}} $ $ =\frac{2\times (360)}{\frac{360}{72}+\frac{360}{120}+\frac{360}{90}}=\frac{2\times 360}{5+3+4} $ $ =\frac{2\times 360}{12}=60,days $
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