Question
Download Solution PDFRodney can do a piece of work in 8 hours. Amit can do it in 16 hours. With Gopal's help, they complete the work in 4 hours. In how many hours can Gopal alone do three times the same work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Rodney can do the work in 8 hours
Amit can do it in 16 hours
All three (Rodney, Amit, and Gopal) together can do it in 4 hours
Calculation:
Assume total work = LCM of 8, 16, and 4 = 16 units
Rodney's efficiency = 16 ÷ 8 = 2 units/hour
Amit's efficiency = 16 ÷ 16 = 1 unit/hour
Total efficiency of Rodney, Amit, and Gopal = 16 ÷ 4 = 4 units/hour
Gopal's efficiency
Gopal's efficiency = Total efficiency - Rodney - Amit = 4 - 2 - 1 = 1 unit/hour
Time taken by Gopal to do 3 times the work
Total work = 3 × 16 = 48 units
Gopal does 1 unit/hour
Time = 48 ÷ 1 = 48 hours
∴ Gopal alone can do 3 times the work in 48 hours.
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