Question

A can do a work in 20 days and B can do it in 10 days. A starts the work and works alone for 5 days. Then B joins A and they finish the work. In how many days total does the work get finished?

• A. 10
• B. 12
• C. 9
• D. 8

Hint:

Calculate individual work rates, then sum them for combined work rate.
Use remaining work and combined rate to find remaining time.

Answer 1

The Correct Option is A

Step 1: Find daily work rate of A and B
- A can complete work in 20 days, so A's work rate = $\frac{1}{20}$ work/day
- B can complete work in 10 days, so B's work rate = $\frac{1}{10}$ work/day
Step 2: Work done by A alone in 5 days
Work done by A in 5 days = $5 \times \frac{1}{20} = \frac{5}{20} = \frac{1}{4}$
Step 3: Remaining work
Remaining work = $1 - \frac{1}{4} = \frac{3}{4}$
Step 4: Combined daily work rate of A and B
Combined rate = $\frac{1}{20} + \frac{1}{10} = \frac{1}{20} + \frac{2}{20} = \frac{3}{20}$ work/day
Step 5: Time taken by A and B together to complete remaining work
Time = $\frac{\text{Work}}{\text{Rate}} = \frac{3/4}{3/20} = \frac{3}{4} \times \frac{20}{3} = 5$ days
Step 6: Total time
Total time = 5 days (A alone) + 5 days (A and B together) = 10 days
Hence, the work is completed in 10 days.