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A and B working together can complete a piece of work in 2 days. B alone can complete the same work in 4 days. How long (in days) will A alone take to
Question

A and B working together can complete a piece of work in 2 days. B alone can complete the same work in 4 days. How long (in days) will A alone take to complete double the work?

A.

4

B.

8

C.

9

D.

11

Correct option is B

Given
Time taken by (A + B) = 2 days
Time taken by B alone = 4 days
Target = Double the work by A alone
Formula Used
​1A+1B=1A+B\frac{1}{A} + \frac{1}{B} = \frac{1}{A+B}​​
Solution
Let A's one day work be 1A.\frac{1}{A}.​​
​1A+14=12 1A=12−14=14\frac{1}{A} + \frac{1}{4} = \frac{1}{2} \\\ \\\frac{1}{A} = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}​​
Time taken by A alone to complete the original work = 4 days
Time taken by A to complete double the work = 4 × 2 = 8 days
Final Answer
So the correct answer is (b)

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