Question : Working alone, A can do the task in 27 hours and B can do it in 54 hours. Find C's share (in Rs.) if A, B, and C get paid Rs. 4,320 for completing a task in 12 hours on which they worked together.
Option 1: 1440
Option 2: 960
Option 3: 1920
Option 4: 1280
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Correct Answer: 1440
Solution :
A can do the task in 27 hours and B can do it in 54 hours.
With C, together, they complete a task in 12 hours.
LCM of 27, 54, and 12 is 108.
Let the total work be 108 units.
A's working efficiency = $\frac{108}{27}$ = 4
B's working efficiency = $\frac{108}{54}$ = 2
A and B and C's combined working efficiency = $\frac{108}{12}$ = 9
⇒ C's working efficiency = 9 – 4 – 2 = 3
So, C's share =$\frac{3}{9}×4320$ = Rs. 1440
Hence, the correct answer is 1440.
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