Question : A can do 50% of the job in 16 days. B can do $\frac{1}{4}$th of the job in 24 days. In how many days can they do $\frac{3}{4}$th of the job working together?
Option 1: 24
Option 2: 9
Option 3: 21
Option 4: 18
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Correct Answer: 18
Solution :
A can complete the job in 32 days (since 50% of the job takes 16 days) and B can complete the job in 96 days (since 25% of the job takes 24 days).
The combined rate of A and B is the sum of their rates.
The time required by, A and B to complete the job in one day,
$=\frac{1}{\frac{1}{32} + \frac{1}{96} }= \frac{96}{4} = 24$ days
The time taken by them to complete $\frac{3}{4}$th of the job, they will take $\frac{3}{4}$ × 24 = 18 days
Hence, the correct answer is 18.
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