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Rakshit, Ajay, and Satish are sanitation workers in a Municipal Corporation. Rakshit alone takes 20 hours to clean a drain while Ajay takes 12 hours when working alone to do the same. All three together take only 5 hours to clean the drain. In how many hours, can Satish complete the work alone?
12
10
15
18
- Rakshit cleans the drain in 20 hours alone. His work rate is 1/20 of the drain per hour.
- Ajay takes 12 hours. His rate is 1/12 of the drain per hour.
- All three together take 5 hours, so their combined rate is 1/5 of the drain per hour.
- We need to find Satish's work rate. When all work together, their combined rate is the sum of individual rates: 1/20 + 1/12 + 1/S = 1/5.
- Solve for Satish's rate (1/S):
- Find a common denominator for the fractions: 60.
- Convert work rates: (3/60 + 5/60 + 1/S = 12/60).
- Combine and solve: (8/60 + 1/S = 12/60).
- (1/S = 4/60, so S = 15).
- Option 3, 15 hours, is correct.
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