Ram and Ramesh can do a work in 12 days, Ramesh and Somesh in 15 days and Somesh and Ram in 10 days. If Ram, Ramesh and Somesh work together, in how many days will they complete the work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 8.
Ram and Ramesh together can complete the work = 12 days
Ram and Ramesh's work rate = 1/12
Ramesh and Somesh together can complete the work = 15 days
Ramesh and Somesh's work rate = 1/15
Somesh and Ram together can complete the work = 10 days
Somesh and Ram's work rate = 1/10
Hence¸
⇒ (Ram + Ramesh) + (Ramesh + Somesh) + (Somesh + Ram) = 1/12 + 1/15 + 1/10
⇒ 2(Ram + Ramesh + Somesh) = 5/60 + 4/60 + 6/60 = 15/60
⇒ 2(Ram + Ramesh + Somesh) = 15/60 = 1/4
⇒ Ram + Ramesh + Somesh = 1/4 × 1/2 = 1/8
Thus, Ram, Ramesh, and Somesh together can complete the work in 8 days.