Question 107

A and B together can complete a work in 30 day. They started together but after 6 days A left the work and the work is completed by B after 36 more days. A alone can complete the entire work in how many days?

Solution

Let total work to be done = L.C.M. (30,36) = 180 units

=> (A+B)'s 1 day's work = $$\frac{180}{30}=6$$ units/day

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

According to ques, => $$(6\times6)+(36\times b)=180$$

=> $$36b=180-36=144$$

=> $$b=\frac{144}{36}=4$$

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

$$\therefore$$ Time taken by A working alone = $$\frac{180}{2}=90$$ days

=> Ans - (B)

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