Question

A is 50% more efficient than B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in approximately:

• A. 13 days
• B. 15 days
• C. 20 days
• D. 30 days

Hint:

Find C's rate first from the 40 day figure, then split A and B in the ratio 3 to 2.

Answer 1

The Correct Option is A

Step 1: Let the whole work be 1 unit. Since C alone completes it in 40 days, C's rate \( = \dfrac{1}{40} \) per day.
Step 2: C does half of what A and B do together, so the combined rate of A and B \( = 2 \times \dfrac{1}{40} = \dfrac{1}{20} \) per day.
Step 3: A is 50% more efficient than B, so if B's rate is \( x \), A's rate is \( 1.5x \). Then \( x + 1.5x = \dfrac{1}{20} \Rightarrow 2.5x = \dfrac{1}{20} \Rightarrow x = \dfrac{1}{50} \).
Step 4: Combined rate of A, B and C \( = \dfrac{1}{20} + \dfrac{1}{40} = \dfrac{2}{40} + \dfrac{1}{40} = \dfrac{3}{40} \) per day.
Step 5: Time taken together \( = \dfrac{40}{3} \approx 13.3 \) days.
Answer: approximately 13 days.