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

Step 1: Set up the rates.
Let total work \(=15\) units, so A's rate \(=1\) unit/day (finishing in 15 days). Since B is twice as efficient as A, B's rate \(=2\) units/day.

Step 2: Set up variables for the timeline.
Let A work alone for x days, then A and B work together for the remaining \((11-x)\) days (since the whole job took 11 days from the start).

Step 3: Set up the work equation.
Work by A alone \(=1\times x=x\) units. Work by both together \(=(1+2)\times(11-x)=3(11-x)=33-3x\) units. Total work: \(x+33-3x=15\).

Step 4: Solve for x.
\(33-2x=15 \Rightarrow 2x=18 \Rightarrow x=9\).

Step 5: Find the days worked together.
Days together \(=11-x=11-9=2\).

Step 6: Final Answer.
They worked together for 2 days, so option B is correct.