Arun and Amit can do a piece of work in 9 days and 12 days respectively . If they work for alternate days and Amit starts the work first , then in how many days 35/36 parts of whole work will be completed ?

Options

A. 10 days
B. 12 days
C. 5 days
D. 8 days

Answer

To solve the problem step by step, we need to determine how much work Arun and Amit can complete together when they work on alternate days, starting with Amit.

### Step-by-Step Solution:

1. **Determine the Work Done by Each Person in One Day:**
- Arun can complete the work in 9 days, so he does \( \frac{1}{9} \) of the work in one day.
- Amit can complete the work in 12 days, so he does \( \frac{1}{12} \) of the work in one day.

2. **Convert to a Common Work Unit:**
- To make calculations easier, we can find a common unit of work. The least common multiple (LCM) of 9 and 12 is 36.
- In 36 units of work:
- Arun does \( \frac{36}{9} = 4 \) units of work in one day.
- Amit does \( \frac{36}{12} = 3 \) units of work in one day.

3. **Calculate Work Done in Two Days:**
- In the first day, Amit works and completes 3 units.
- In the second day, Arun works and completes 4 units.
- Therefore, in 2 days, they complete \( 3 + 4 = 7 \) units of work.

4. **Determine the Total Work Needed:**
- The total work is 36 units.
- We need to find out how many days it takes to complete \( \frac{35}{36} \) of the work.
- \( \frac{35}{36} \) of the total work is \( 35 \) units.

5. **Calculate How Many Sets of 2 Days are Needed:**
- Since they complete 7 units in 2 days, we can find how many sets of 2 days are needed to complete 35 units.
- To find the number of sets, we divide 35 by 7:
\[ \frac{35}{7} = 5 \text{ sets of 2 days} \]

6. **Calculate Total Days Taken:**
- Each set of 2 days takes 2 days, so for 5 sets:
\[ 5 \times 2 = 10 \text{ days} \]

### Final Answer:
Thus, it will take **10 days** to complete \( \frac{35}{36} \) of the work.