Kamal and Anil can dig a pond in 8 days and 14 days respectively. If the total expense of digging in Rs 4400 then how much money will Anil earn?

Options

A. 1400
B. 1600
C. 1500
D. 1300

Answer

To solve the problem, we need to determine how much money Anil will earn from the total expense of Rs 4400 based on the work done by him and Kamal.

### Step-by-Step Solution:

1. **Determine the Work Rate of Kamal and Anil:**
- Kamal can dig the pond in 8 days. Therefore, his work rate is \( \frac{1}{8} \) of the pond per day.
- Anil can dig the pond in 14 days. Therefore, his work rate is \( \frac{1}{14} \) of the pond per day.

2. **Calculate the Total Work Done in One Day:**
- The combined work rate of Kamal and Anil in one day is:
\[ \text{Combined Work Rate} = \frac{1}{8} + \frac{1}{14} \]
- To add these fractions, find a common denominator. The least common multiple of 8 and 14 is 56.
- Convert each fraction:
\[ \frac{1}{8} = \frac{7}{56}, \quad \frac{1}{14} = \frac{4}{56} \]
- Now, add the two fractions:
\[ \text{Combined Work Rate} = \frac{7}{56} + \frac{4}{56} = \frac{11}{56} \]

3. **Determine the Total Work in Terms of Days:**
- Since they can complete the pond together at a rate of \( \frac{11}{56} \) of the pond per day, the total time taken to complete the pond is:
\[ \text{Total Days} = \frac{1 \text{ pond}}{\frac{11}{56} \text{ pond/day}} = \frac{56}{11} \text{ days} \]

4. **Calculate the Work Done by Each Individual:**
- Work done by Kamal in \( \frac{56}{11} \) days:
\[ \text{Work by Kamal} = \frac{56}{11} \times \frac{1}{8} = \frac{56}{88} = \frac{7}{11} \]
- Work done by Anil in \( \frac{56}{11} \) days:
\[ \text{Work by Anil} = \frac{56}{11} \times \frac{1}{14} = \frac{56}{154} = \frac{4}{11} \]

5. **Calculate the Earnings Based on Work Done:**
- The total expense of digging the pond is Rs 4400. The earnings for Anil can be calculated based on the proportion of work done:
\[ \text{Anil's Earnings} = \text{Total Expense} \times \frac{\text{Work by Anil}}{\text{Total Work}} = 4400 \times \frac{4/11}{1} = 4400 \times \frac{4}{11} \]
- Simplifying this:
\[ \text{Anil's Earnings} = 4400 \times \frac{4}{11} = 1600 \]

### Final Answer:
Anil will earn Rs 1600.