Amit, Vipul and Kapil can do a piece of work in 12, 16 and 24 days, respectively. If they complete the work together and get an amount of Rs. 2700, then what is the share of Vipul in that amount?

Options

A. X 450
B. X 1000
C. X 225
D. X 900

Answer

To solve the problem, we need to determine the share of Vipul from the total amount of Rs. 2700 based on the work efficiency of Amit, Vipul, and Kapil.

### Step-by-Step Solution:

1. **Determine the Work Rates**:
- Amit can complete the work in 12 days, so his work rate is \( \frac{1}{12} \) of the work per day.
- Vipul can complete the work in 16 days, so his work rate is \( \frac{1}{16} \) of the work per day.
- Kapil can complete the work in 24 days, so his work rate is \( \frac{1}{24} \) of the work per day.

2. **Calculate the Least Common Multiple (LCM)**:
- To find a common time frame for their work rates, we calculate the LCM of 12, 16, and 24.
- The LCM of 12, 16, and 24 is 48.

3. **Calculate the Work Done in 48 Days**:
- In 48 days:
- Amit would complete \( \frac{48}{12} = 4 \) units of work.
- Vipul would complete \( \frac{48}{16} = 3 \) units of work.
- Kapil would complete \( \frac{48}{24} = 2 \) units of work.

4. **Calculate Total Work Done**:
- Total work done by all three together in 48 days = \( 4 + 3 + 2 = 9 \) units of work.

5. **Determine the Share of Each Worker**:
- The total amount to be distributed is Rs. 2700.
- The share of Vipul is based on his contribution to the total work.
- Vipul's share = \( \frac{\text{Work done by Vipul}}{\text{Total work done}} \times \text{Total amount} \)
- Vipul's share = \( \frac{3}{9} \times 2700 \)

6. **Calculate Vipul's Share**:
- Vipul's share = \( \frac{1}{3} \times 2700 = 900 \)

### Final Answer:
Vipul's share in the amount is Rs. 900.

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