Question

A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

• A. 45
• B. 75
• C. 60
• D. 90

Answer 1

Answer:

C. 60

Concepts in Time and Work

Understanding Work Rate

• If a person can complete a work in 'x' days, their work rate is 1/x of the work per day.

• The total work is considered as 1 unit.

Applying the Concepts to the Problem

• Let the number of days A takes to finish the work alone be 'a' days.

• Let the number of days B takes to finish the work alone be 'b' days.

• Work done by A in 1 day = 1/a

• Work done by B in 1 day = 1/b

• Together, their work rate is (1/a + 1/b) per day.

Problem Breakdown and Calculation

1. A and B together finish the work in 30 days.

2. So, their combined work rate is 1/30 work per day.

3. They worked together for 20 days. Work done in these 20 days = 20 × (1/30) = 2/3 of the work.

4. Remaining work = 1 - 2/3 = 1/3 of the work.

5. After B left, A worked alone for another 20 days to finish the remaining 1/3 work.

6. This implies that A alone can do 1/3 of the work in 20 days.

7. Therefore, A alone can finish the entire work (3/3) in 20 days × 3 = 60 days.