Question : A can do a piece of work in 24 days and B can do the same work in 30 days. If they work on it together for 8 days, then the fraction of the work that is left is:
Option 1: $\frac{2}{3}$
Option 2: $\frac{2}{5}$
Option 3: $\frac{3}{5}$
Option 4: $\frac{1}{3}$
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Correct Answer: $\frac{2}{5}$
Solution :
A can do the work in 24 days, so A's work rate is $\frac{1}{24}$ of the work per day.
B can do the work in 30 days, so B's work rate is $\frac{1}{30}$ of the work per day.
When A and B work together, their combined work rate is the sum of their work rates:
$\frac{1}{24} + \frac{1}{30} = \frac{5+4}{120} = \frac{9}{120} = \frac{3}{40}$
In 8 days, A and B can complete $\frac{3}{40}\times 8$ of the work which is equal to $\frac{3}{5}$ of the work.
$\therefore$ Work left $=1-\frac{3}{5} = \frac{2}{5}$
Hence, the correct answer is $\frac{2}{5}$.
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