Question

P works twice as fast as Q. Q alone can complete some work in 12 days. Working together, how long will P and Q take to complete the work?

• A. 8 days
• B. 4 days
• C. 6 days
• D. 10 days

Answer 1

Answer:

B. 4 days

1. Find P's work rate:

• Since P works twice as fast as Q, P can complete the same work in half the time.

• P alone can complete the work in 12 days / 2 = 6 days.

2. Calculate individual work rates:

• Q's work rate: Q completes 1/12 of the work per day.

• P's work rate: P completes 1/6 of the work per day.

3. Calculate combined work rate:

• Combined work rate = P's work rate + Q's work rate

• Combined work rate = (1/6) + (1/12) = 3/12 = 1/4

4. Find the time taken together:

• Time taken to complete the work together = 1 / Combined work rate

• Time taken = 1 / (1/4) = 4 days

Therefore, working together, P and Q will take 4 days to complete the work.