A can do a work in 12 days while B can do it in 15 days. They undertake to complete it together for ₹450, what will be the share of A in this amount of money?
A एक कार्य को 12 दिन में पूरा कर सकता है जबकि B उसे 15 दिन में पूरा कर सकता है। वे उसे एक साथ मिलकर ₹450 में करने को तैयार हो जाते है। इस धनराशि में A का हिस्सा कितना होगा ?

Options

A. ₹200
B. ₹240
C. ₹250
D. ₹300

Explanation

To solve the problem, we need to determine the share of A in the total amount of ₹450 based on the work efficiency of A and B.

### Step-by-Step Solution:

1. **Determine the work rates of A and B:**
- A can complete the work in 12 days, so A's work rate is \( \frac{1}{12} \) of the work per day.
- B can complete the work in 15 days, so B's work rate is \( \frac{1}{15} \) of the work per day.

2. **Calculate the combined work rate of A and B:**
- The combined work rate of A and B is:
\[ \text{Combined work rate} = \frac{1}{12} + \frac{1}{15} \]
- To add these fractions, find a common denominator. The least common multiple of 12 and 15 is 60.
\[ \frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60} \]
- Therefore,
\[ \text{Combined work rate} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20} \]

3. **Calculate the ratio of work done by A and B:**
- The work done by A in one day is \( \frac{1}{12} \) and by B is \( \frac{1}{15} \).
- The ratio of their work rates (A : B) can be calculated as:
\[ A : B = \frac{1/12}{1/15} = \frac{15}{12} = \frac{5}{4} \]

4. **Determine the total parts in the ratio:**
- The total parts in the ratio of A to B is \( 5 + 4 = 9 \).

5. **Calculate A's share of the total amount:**
- The total payment for the work is ₹450.
- A's share is calculated as:
\[ \text{A's share} = \left(\frac{5}{9}\right) \times 450 \]
- Performing the calculation:
\[ \text{A's share} = \frac{5 \times 450}{9} = \frac{2250}{9} = 250 \]

### Final Answer:
A's share in the amount of ₹450 will be ₹250.