Question 52

K alone can complete a work in 20 days and M alone can complete the same work in 30 days. K and M start the work together but K leaves the work after 5 days of the starting of work. In how many days M will complete the remaining work?

Solution

Let total work to be done = L.C.M. (20,30) = 60 units

K can complete it in 20 days, => K's efficiency = $$\frac{60}{20}=3$$ units/day

Similarly, M's efficiency = $$\frac{60}{30}=2$$ units/day

=> Work done in 5 days together = $$(3+2)\times5=25$$ units

Let M complete the remaining work in $$t$$ days

=> $$25+2t=60$$

=> $$t=\frac{35}{2}$$ days

=> Ans - (A)

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