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Q.

A and B can independently finish a piece of work in 36 days and 45 days respectively. They started working together and after a few days A left. After that B could finish the remaining work in 36 days. After how many days of working did A leave?

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a

3 days

b

6 days

c

4 days

d

5 days

answer is D.

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Detailed Solution

Total work $= L C M$ of $(36, 45) = 180$ units Efficiency of $A = \frac{180}{36} = 5$
Efficiency of $B = \frac{180}{45} = 4$
B's work in $36$ days $= 36 \times 4 = 144$ units Remaining work $= 180 - 144 = 36$ units
Hence, A leaves after $= \frac{36}{5 + 4} = 4$ days

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A and B can independently finish a piece of work in 36 days and 45 days respectively. They started working together and after a few days A left. After that B could finish the remaining work in 36 days. After how many days of working did A leave?