Question 58

A can do a piece of work in 10 days and B in 12 days. With help of C, they finish the work in 4 days. In how many days C alone can do the same work?

Solution

Let total work is L.C.M. (10,12,4) = 60 units

A alone can complete a work in 10 days, => A's efficiency = $$\frac{60}{10}=6$$ units/day

Similarly B's efficiency = $$\frac{60}{12}=5$$ units/day

Now, (A+B+C)'s efficiency = $$\frac{60}{4}=15$$ units/day

=> C's efficiency = $$15-(6+5)=4$$ units/day

$$\therefore$$ Days required by C alone to complete the work = $$\frac{60}{4}=15$$ days

=> Ans - (B)

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