Aman and Ajay can build a wall in 9 days and 12 days respectively. In how many days can they finish the work if they work together ?
A. `5(1)/(7)`
B. `11(1)/(2)`
C. 2
D. 7

Options

A. C
B. B
C. D
D. A

Answer

To find out how many days Aman and Ajay can finish building the wall if they work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- Aman can complete the wall in 9 days. Therefore, his work rate is:
\[ \text{Aman's work rate} = \frac{1}{9} \text{ of the wall per day} \]
- Ajay can complete the wall in 12 days. Therefore, his work rate is:
\[ \text{Ajay's work rate} = \frac{1}{12} \text{ of the wall per day} \]

### Step 2: Add their work rates to find the combined work rate.
- When Aman and Ajay work together, their combined work rate is:
\[ \text{Combined work rate} = \frac{1}{9} + \frac{1}{12} \]
- To add these fractions, we need a common denominator. The least common multiple of 9 and 12 is 36. Therefore:
\[ \frac{1}{9} = \frac{4}{36} \quad \text{and} \quad \frac{1}{12} = \frac{3}{36} \]
- Now, adding these fractions:
\[ \text{Combined work rate} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36} \]

### Step 3: Calculate the time taken to complete the work together.
- If their combined work rate is \(\frac{7}{36}\) of the wall per day, the time taken to complete 1 whole wall is the reciprocal of their combined work rate:
\[ \text{Time} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{7}{36}} = \frac{36}{7} \text{ days} \]
- This can be converted to a mixed number:
\[ \frac{36}{7} = 5 \frac{1}{7} \text{ days} \]

### Final Answer:
Aman and Ajay can finish building the wall together in \(5 \frac{1}{7}\) days.

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