Question 107

A and B together can complete a work in 10 days. They started together but A left after 2 days and the remaining work was completed by B in 12 days. In how many days can A complete the entire work while working alone?

Solution

Let total work to be done = L.C.M. (10,12) = 60 units

=> (A+B)'s 1 day's work = $$\frac{60}{10}=6$$ units/day

Let B's efficiency = $$b$$ units/day

According to ques, => $$(2\times6)+(12\times b)=60$$

=> $$12b=60-12=48$$

=> $$b=\frac{48}{12}=4$$

Thus, A's efficiency = $$6-4=2$$ units/day

$$\therefore$$ Time taken by A working alone = $$\frac{60}{2}=30$$ days

=> Ans - (C)

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