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Anuj is 3 times faster than Ramesh. Ramesh can finish a work alone in 48 days. If Anuj and Ramesh started working together and Anuj left the work 4 days before the completion time. How much time will it take to complete the work?

Anuj is 3 times faster than Ramesh. Ramesh can finish a work alone in 48 days. If Anuj and Ramesh started working together and Anuj left the work 4 days before the completion time. How much time will it take to complete the work? Correct Answer 15 days

∵ Efficiency is always inversely proportional to time and Anuj is 3 times faster than Ramesh.

Time taken by Ramesh = 48 days

⇒ Time taken by Anuj = 48 × (1/3) = 16 days

Suppose total work = LCM of 16 and 48 = 48 units

⇒ Efficiency of Ramesh = 48/48 = 1 unit/day

⇒ Efficiency of Anuj = 48/16 = 3 units/day

Anuj left 4 days before the stipulated time i.e. Ramesh worked for last 4 days

Work done by ramesh in 4 days = 4 × 1 = 4 units

But the remaining work was completed by both anuj and ramesh.

Remaining work = 48 - 4 = 44 units

⇒ Time required to complete 44 units by ramesh and anuj together

= 44/4 = 11 days

∴ Total time taken to complete the work =  4 + 11 = 15 days

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