Question

B is twice 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 starting. For how many days did they work together?

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

Answer 1

The Correct Option is B

To solve this problem, we need to determine how many days A and B worked together to complete the task in 11 days.

Step 1: Calculate A's work rate.
A can complete the work in 15 days. Therefore, A's work rate is \( \frac{1}{15} \) of the work per day.

Step 2: Calculate B's work rate.
B is twice as efficient as A, so B can do \( 2 \times \frac{1}{15} = \frac{2}{15} \) of the work per day.

Step 3: Set up the equation based on the combined work.
Let \( x \) be the number of days A worked alone, and \( 11 - x \) be the days A and B worked together. The equation for the work done is:
\( \frac{x}{15} + (11-x)(\frac{1}{15} + \frac{2}{15}) = 1 \)

Step 4: Simplify and solve the equation.
\( \frac{x}{15} + (11-x)\frac{3}{15} = 1 \)
\( \frac{x}{15} + \frac{33-3x}{15} = 1 \)
\( \frac{x + 33 - 3x}{15} = 1 \)
\( \frac{33-2x}{15} = 1 \)
\( 33 - 2x = 15 \)
\( 2x = 18 \)
\( x = 9 \)

Step 5: Determine the number of days A and B worked together.
A worked for 9 days alone, so they worked together for \( 11 - 9 = 2 \) days.

Therefore, A and B worked together for 2 days.