Question

Raman and Sahil working together could complete a work in 35 days and with the heḥ of Arun they could
complete it in 28 days. How long would Arun take to complete the work alone?
70 days
140 days
210 days
280 days​

Answer 1

Given :- Raman and Sahil working together could complete a work in 35 days and with the help of Arun they could complete it in 28 days. How long would Arun take to complete the work alone ?

A) 70 days

B) 140 days

C) 210 days

D) 280 days.

Solution :-

LCM of 35 and 28 = 140 unit = Let total work.

So,

→ Efficiency of Raman and sahil together = (Total work) / (Time taken by both of them together) = 140/35 = 4 unit/day.

Similarly,

→ Efficiency of (Raman + sahil + Arun) = (Total work) / (Time taken by all three together) = 140/28 = 5 unit / day.

Therefore,

→ Efficiency of Arun = (Raman + sahil + Arun) - (Raman + sahil) = 5 - 4 = 1 unit / day.

Hence,

→ Time taken by arun alone to complete the work = (Total work) / (Efficiency of Arun) = 140/1 = 140 days. (Option B) (Ans.)

∴ Arun takes 140 days to complete the work alone.

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