Ram and Shyam can separately finish a piece of work in 20 days and 15 days. Both worked together for 6 days, thereafter Shyam was replaced by Mohan. If the rest work was finished in next 4 days, then how many months will Mohan alone take to complete the work?

40 days

Total efficiency of Ram and Shyam = 3 + 4 = 7

Work done by Ram and Shyam in 6 days = 6 × 7 = 42

Remaining work = 60 - 42 = 18

Remaining work done by Ram and Mohan in 4 days.

Therefore,

⇒ Efficiency : (Ram + Mohan) = \(\frac{18}{4}\) = \(\frac{9}{2}\)

⇒ Eff. of Mohan = \(\frac{9}{2}\) - 3 = \(\frac{3}{2}\)

Mohan alone will finish complete work = \(\frac{60}{\frac{3}{2}}\) = 40 days