A can finish a work in 36 months, B in 18 months and C in 24 months. B and C start the work but are forced to leave after 4 months. The remaining work was done by A in 22 months.

24 months

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11 months

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Solution

The correct option is A
24 months

A`s 1 month`s work = $\frac{1}{36}$
B`s 1 month`s work = $\frac{1}{18}$
C`s 1 month`s work = $\frac{1}{24}$
(B + C)`s 1 month`s work
= $\frac{1}{18} + \frac{1}{24} = \frac{7}{72}$ [LCM of 18 and 24 = 72]

Work done by B and C in 4 months = $\frac{7}{72} \times 4 = \frac{7}{18}$

Remaining work = $1 - \frac{7}{18} = \frac{18 - 7}{18} = \frac{11}{18}$

Now, $\frac{1}{36}$ work is done by A in 1 month

So, $\frac{11}{18}$ work is done by A in $36 \times \frac{11}{18} = 22$ months
So, the remaining work was done by A in 22 months.

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