Question : A alone can do a work in 25 days and B alone can do the same work in 40 days. They worked together and were paid a total of Rs. 5200. What is the difference between their shares?
Option 1: Rs. 1000
Option 2: Rs. 800
Option 3: Rs. 1200
Option 4: Rs. 600
Correct Answer: Rs. 1200
Solution :
Since efficiency is inversely proportional to the time taken to finish a work.
⇒ $\frac{\text{Efficiency of A}}{\text{Efficiency of B}} = \frac{\text{Time taken by B}}{\text{Time taken by A}} = \frac{40}{25}= \frac{8}{5}$
Money will be distributed among the workers in terms of efficiency if they have worked for equal time.
⇒ $\frac{\text{Share of A}}{\text{Share of B}} = \frac{8}{5}$
Now, Divide Rs. 5200 in the ratio of 8 : 5.
⇒ Share of A = $\frac{8}{13}$ × 5200 = Rs. 3200
⇒ Share of B = $\frac{5}{13}$ × 5200 = Rs. 2000
Difference = A's share – B's share = 3200 – 2000 = Rs. 1200
Hence, the correct answer is Rs. 1200.
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