Question : 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?
Option 1: 12
Option 2: 10
Option 3: 15
Option 4: 18
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Correct Answer: 15
Solution :
Given: Rakshit takes 20 hours to clean a drain.
Ajay takes 12 hours to clean the drain.
Rakshit, Ajay, and Satish take 5 hours to clean the drain.
Total work = LCM of (20, 12, 5) = 60 units
Efficiency of Rakshit = $\frac{60}{20}$ = 3 units/hours
Efficiency of Ajay = $\frac{60}{12}$ = 5 units/hours
Efficiency of Rakshit, Ajay, and Satish = $\frac{60}{5}$ = 12 units/hours
Efficiency of Satish = 12 – 8 = 4 units/hours
Time taken by Satish to complete the work = $\frac{60}{4}$ = 15 hours
Hence, the correct answer is 15.
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