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
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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