Question : Robert takes twice as much time as Tom and thrice as much time as George to complete a work. If working together, they can complete it in 23 hours, then find the time that Tom will take to complete the work.
Option 1: 46 hours
Option 2: 69 hours
Option 3: 11 hours
Option 4: 39 hours
Correct Answer: 69 hours
Solution :
Given: Robert takes twice as much time as Tom and thrice as much time as George to complete a work.
Working together, they can complete it in 23 hours.
Work = Time × Efficiency
According to the question,
$\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{1}{23}$
⇒ $\frac{1+2+3}{x}=\frac{1}{23}$
⇒ $\frac{6}{x}=\frac{1}{23}$
⇒ $x=138$
The time that Tom will take to complete the work = $\frac{138}{2}=69$ hours
Hence, the correct answer is 69 hours.
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