Question

A can complete a work in 15 days and B can complete the same work in 45 days . Together, they can complete the same work in

• A. 12.25 days
• B. 11.5 days
• C. 12.5 days
• D. 11.25 days

Hint:

Alternatively, use the LCM method:
Assume the total work is the LCM of 15 and 45, which is 45 units.
- A's daily efficiency = $45 \div 15 = 3$ units/day.
- B's daily efficiency = $45 \div 45 = 1$ unit/day.
- Combined daily efficiency = $3 + 1 = 4$ units/day.
- Time taken = $\frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{45}{4} = 11.25$ days.

Answer 1

The Correct Option is D

Step 1: Find individual work rates per day.
A completes the work in 15 days, so A's rate = 1/15 per day. B completes it in 45 days, so B's rate = 1/45 per day.
Step 2: Find their combined rate.
\[ \text{Combined rate} = \frac{1}{15} + \frac{1}{45} = \frac{3}{45} + \frac{1}{45} = \frac{4}{45} \text{ per day} \]
Step 3: Calculate days needed together.
\[ \text{Days} = \frac{45}{4} = 11.25 \text{ days} \] \[ \boxed{11.25} \]