'A' can complete the 60% of the work in 9 days, while 'B' can complete the work in `7 1/2` days. If they work together, then in how many days will the work be completed?

Options

A. 7
B. 6
C. 5
D. 0.04

Answer

To solve the problem, we need to determine how much work 'A' and 'B' can complete together in a day and then find out how many days it will take them to finish the entire work.

### Step-by-Step Solution:

1. **Calculate the total work done by 'A':**
- 'A' completes 60% of the work in 9 days.
- Therefore, the total work (let's denote it as W) can be calculated as:
\[ 0.6W = \text{Work done by A in 9 days} \]
\[ W = \frac{0.6W}{0.6} = \frac{9}{0.6} = 15 \text{ days (for 100% work)} \]

2. **Calculate the work rate of 'A':**
- If 'A' completes the entire work in 15 days, then the work rate of 'A' is:
\[ \text{Rate of A} = \frac{1}{15} \text{ (work per day)} \]

3. **Calculate the work rate of 'B':**
- 'B' can complete the work in \(7 \frac{1}{2}\) days, which is equal to \(7.5\) days.
- Therefore, the work rate of 'B' is:
\[ \text{Rate of B} = \frac{1}{7.5} = \frac{2}{15} \text{ (work per day)} \]

4. **Calculate the combined work rate of 'A' and 'B':**
- When 'A' and 'B' work together, their combined work rate is:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = \frac{1}{15} + \frac{2}{15} = \frac{3}{15} = \frac{1}{5} \text{ (work per day)} \]

5. **Calculate the total time taken to complete the work together:**
- If they complete \(\frac{1}{5}\) of the work in one day, then the total time taken to complete the entire work (1 unit of work) is:
\[ \text{Time} = \frac{1 \text{ (total work)}}{\frac{1}{5} \text{ (work per day)}} = 5 \text{ days} \]

### Final Answer:
Thus, 'A' and 'B' together will complete the work in **5 days**.