Question

B is twice as efficient as A, and A can do a piece of work in 15 days. A started the work, and after a few days B joined him. They completed the work in 11 days from the start. For how many days did they work together?

• A. 1 day
• B. 2 days
• C. 6 days
• D. 5 days

Hint:

Each day B joins adds 2 extra units over what A alone would do; find how many such days are needed to cover the shortfall from 11 days of A working alone.

Answer 1

The Correct Option is B

Since B's rate is double A's, it helps to imagine the last stretch of work as being done at 3 times A's solo pace, and work out how much “extra” that stretch contributes compared to A working alone the whole time.

1. If A had worked alone for all 11 days, A would complete $11 \times 1 = 11$ units, but the actual total work is $15$ units, a shortfall of $15 - 11 = 4$ units.
2. Each day that B works alongside A (instead of A working alone that day) adds an extra $2$ units beyond what A alone would have done that day (since together they do 3 units instead of A's 1 unit, a gain of 2).
3. To make up the shortfall of 4 units at a gain of 2 units per joint day, the number of joint days must be $\frac{4}{2} = 2$.

So the correct answer is option B, 2 days.