Question : If A had worked alone, it would have taken him 63 hours to complete the task. What is B's share if A and B work together on a task, finishing it in 36 hours, and they get paid Rs. 5,950 for it?
Option 1: Rs. 3,400
Option 2: Rs. 3,600
Option 3: Rs. 2,550
Option 4: Rs. 2,750
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Correct Answer: Rs. 2,550
Solution :
A can do the work in 63 hours.
A and B can do the work in 36 hours.
So, B can do the work alone in = $\frac{1}{\text{1 day work of A and B – 1 day work of A}}=\frac{1}{\frac{1}{36}-\frac{1}{63}}=\frac{756}{9}=$ 84 hours
Now, the ratio of number of days = 63 : 84 = 3 : 4
So, the ratio of efficiency = 4 : 3
Therefore, share of A = $\frac{4}{7}$ × 5950 = Rs. 3400
Thus, the share of B = Rs. (5990 – 3400) = Rs. 2,550
Hence, the correct answer is Rs. 2,550.
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