Question

B can do a work in 48 days. If A starts the work and after 10 days he leaves, then B alone finishes the remaining work in 42 days. In how many days A and B together will finish the work?

• A. 30
• B. 25
• C. 35
• D. 28

Hint:

To find the time taken when two people are working together, first calculate their individual rates of work and then sum the rates.

Answer 1

The Correct Option is A

Let the total work be \( W \). - B can complete the work in 48 days, so B’s rate of work is: \[ \text{B’s rate} = \frac{W}{48} \] - In the first 10 days, A works alone. Let A’s rate of work be \( \frac{W}{a} \), where \( a \) is the number of days A would take to complete the work alone. The work done by A in the first 10 days is: \[ \text{Work done by A} = 10 \times \frac{W}{a} = \frac{10W}{a} \] After A leaves, B finishes the remaining work in 42 days, so the work done by B in 42 days is: \[ \text{Work done by B} = 42 \times \frac{W}{48} = \frac{7W}{8} \] The total work is \( W \), so the remaining work after 10 days is: \[ W - \frac{10W}{a} = \frac{7W}{8} \] Solving for \( a \): \[ W - \frac{10W}{a} = \frac{7W}{8} \quad \Rightarrow \quad \frac{10W}{a} = \frac{W}{8} \quad \Rightarrow \quad a = 80 \] Thus, A can complete the work in 80 days. Now, we calculate the time taken for A and B to complete the work together. Their combined rate is: \[ \text{Combined rate} = \frac{W}{80} + \frac{W}{48} = \frac{48W + 80W}{80 \times 48} = \frac{128W}{3840} = \frac{W}{30} \] Thus, A and B together will complete the work in \( \boxed{30} \) days.