Rodney can do a piece of work in 8 hours. Amit can do this work in 12 hours. With the help of Gopal, they completed the task in 3 hours. In how many hours can Gopal alone do double the work?

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  1. 18
  2. 16
  3. 15
  4. 17

Answer (Detailed Solution Below)

Option 2 : 16
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Detailed Solution

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Given:

Rodney's time = 8 hours

Amit's time = 12 hours

Combined time (Rodney + Amit + Gopal) = 3 hours

Formula Used:

Efficiency = Total Work / Time taken

Calculation:

LCM of 8 and 12 = 24. Let Total Work = 24 units.

Rodney's efficiency = Total Work / Rodney's time = 24 / 8 = 3 units/hour

Amit's efficiency = Total Work / Amit's time = 24 / 12 = 2 units/hour

Combined efficiency (Rodney + Amit + Gopal) = Total Work / Combined time = 24 / 3 = 8 units/hour

Gopal's efficiency = Combined efficiency - (Rodney's efficiency + Amit's efficiency)

\(\Rightarrow\) Gopal's efficiency = 8 - (3 + 2) = 8 - 5 = 3 units/hour

Double the work = 2 × 24 = 48 units

Time taken by Gopal alone to do double the work = Double the work / Gopal's efficiency = 48 / 3 = 16 hours

Gopal alone can do double the work in 16 hours.

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