Robin can do a work alone in 9 days. Amit can do the same work alone in 6 days. Both of them finish the work together and they get a total Rs 2500. What is the share (in Rs) of Robin?

Options

A. 1700
B. 1200
C. 1500
D. 1000

Explanation

To solve the problem, we need to determine the share of Robin from the total payment of Rs. 2500 based on the amount of work he and Amit can do.

### Step-by-Step Solution:

1. **Calculate Robin's Work Rate:**
Robin can complete the work alone in 9 days. Therefore, his work rate (amount of work done in one day) is:
\[ \text{Robin's 1 day's work} = \frac{1}{9} \]

2. **Calculate Amit's Work Rate:**
Amit can complete the work alone in 6 days. Therefore, his work rate is:
\[ \text{Amit's 1 day's work} = \frac{1}{6} \]

3. **Calculate Combined Work Rate:**
When Robin and Amit work together, their combined work rate is the sum of their individual work rates:
\[ \text{Combined work rate} = \frac{1}{9} + \frac{1}{6} \]
To add these fractions, we need a common denominator. The least common multiple of 9 and 6 is 18.
\[ \frac{1}{9} = \frac{2}{18}, \quad \frac{1}{6} = \frac{3}{18} \]
Therefore,
\[ \text{Combined work rate} = \frac{2}{18} + \frac{3}{18} = \frac{5}{18} \]

4. **Determine the Ratio of Work Done:**
The ratio of work done by Robin and Amit can be calculated using their individual work rates:
\[ \text{Ratio of Robin's work to Amit's work} = \frac{\frac{1}{9}}{\frac{1}{6}} = \frac{6}{9} = \frac{2}{3} \]
This means for every 2 parts of work Robin does, Amit does 3 parts.

5. **Calculate Total Parts of Work:**
The total parts of work done is:
\[ 2 + 3 = 5 \text{ parts} \]

6. **Calculate Robin's Share of Payment:**
Since the total payment is Rs. 2500, Robin's share can be calculated based on the ratio of work done:
\[ \text{Robin's share} = \frac{2}{5} \times 2500 = 1000 \]

### Final Answer:
Robin's share of the payment is Rs. 1000.

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