Question : A and B working together can complete a job in 90 days. The ratio of their efficiencies is 3 : 5. In how many days can the faster person complete the job?
Option 1: 90 days
Option 2: 80 days
Option 3: 144 days
Option 4: 118 days
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Correct Answer: 144 days
Solution : Let the efficiency of A as $3x$ and the efficiency of B as $5x$. The total efficiency of A and B working together = $3x + 5x = 8x$ This means they can complete $8x$ the amount of work in one day. Given that A and B together can complete the job in 90 days. The total work to be done = $90 × 8x$ The faster person is B, with an efficiency of $5x$. The time it would take for B to complete the job alone is the total work divided by B’s efficiency. The time would take for B to complete the job alone = $\frac{90 \times 8x}{5x}$ = 144 days. Hence, the correct answer is 144 days.
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