Question : A is twice as good a workman as B and together they complete a task in 13 days. In how many days will B alone complete the task?
Option 1: 39
Option 2: 42
Option 3: 21
Option 4: 18.5
Correct Answer: 39
Solution :
Let B's efficiency be $x$.
A's efficiency = $2x$
Work done by A and B together in 13 days = 1
Work done by A and B together in 1 day = $\frac{1}{13}$
Work done by A in 1 day + Work done by B in 1 day = $\frac{1}{13}$
⇒ $2x+x=\frac{1}{13}$
⇒ $3x=\frac{1}{13}$
⇒ $x=\frac{1}{39}$
Work done by B in 1 day $=\frac{1}{39}$
Therefore, the work is completed by B in 39 days
Hence, the correct answer is 39.
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