A' can complete a work in 15 days and 'B' can complete the same work in 20 days. Working together, in how many days will they complete 70% of the same work ?

Options

A. 7
B. 6
C. 5
D. 8

Answer

To solve the problem, we need to determine how many days A and B will take to complete 70% of the work when working together.

### Step-by-Step Solution:

1. **Determine the work done by A and B in one day:**
- A can complete the work in 15 days. Therefore, A's work rate (efficiency) is:
\[ \text{Efficiency of A} = \frac{1}{15} \text{ (work per day)} \]
- B can complete the work in 20 days. Therefore, B's work rate (efficiency) is:
\[ \text{Efficiency of B} = \frac{1}{20} \text{ (work per day)} \]

2. **Calculate the combined work rate of A and B:**
- When A and B work together, their combined efficiency is:
\[ \text{Combined Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} = \frac{1}{15} + \frac{1}{20} \]
- To add these fractions, we need a common denominator. The least common multiple of 15 and 20 is 60. Thus:
\[ \frac{1}{15} = \frac{4}{60} \quad \text{and} \quad \frac{1}{20} = \frac{3}{60} \]
- Therefore:
\[ \text{Combined Efficiency} = \frac{4}{60} + \frac{3}{60} = \frac{7}{60} \]

3. **Determine the total work to be completed:**
- We need to find out how much work corresponds to 70% of the total work. Since the total work is considered as 1 (100%), 70% of the work is:
\[ \text{Work to be completed} = 0.7 \text{ (or } \frac{70}{100} = \frac{7}{10}\text{)} \]

4. **Calculate the time taken to complete 70% of the work:**
- Using the formula:
\[ \text{Time} = \frac{\text{Work}}{\text{Efficiency}} \]
- We substitute the work to be completed and the combined efficiency:
\[ \text{Time} = \frac{0.7}{\frac{7}{60}} = 0.7 \times \frac{60}{7} = \frac{42}{7} = 6 \text{ days} \]

### Final Answer:
A and B, working together, will complete 70% of the work in **6 days**.