Rs 4830 is divided among Abhishek, Dishant and Prashant such that if Abhishek's share diminishes by Rs 5, Dishant's share diminishes by Rs 10 and Prashant's share diminishes by Rs 15, their shares will be in the ratio `5 : 4 : 3`. Find the Dishant's originat share?

Options

A. 1610
B. 2010
C. 2410
D. 1590

Answer

To solve the problem, we need to find Dishant's original share when Rs. 4830 is divided among Abhishek, Dishant, and Prashant, given the conditions of diminishing shares.

### Step-by-Step Solution:

1. **Let the Shares be Represented:**
Let Abhishek's share be A, Dishant's share be D, and Prashant's share be P. According to the problem, we have:
\[ A + D + P = 4830 \]

2. **Diminished Shares:**
When Abhishek's share diminishes by Rs. 5, Dishant's by Rs. 10, and Prashant's by Rs. 15, their shares will be in the ratio of 5:4:3. Therefore, we can express their diminished shares as:
\[ A - 5, \quad D - 10, \quad P - 15 \]

3. **Setting Up the Ratio:**
The diminished shares can be expressed in terms of a common variable k:
\[ A - 5 = 5k, \quad D - 10 = 4k, \quad P - 15 = 3k \]

4. **Expressing A, D, and P:**
From the equations above, we can express A, D, and P in terms of k:
\[ A = 5k + 5 \]
\[ D = 4k + 10 \]
\[ P = 3k + 15 \]

5. **Substituting into the Total Share Equation:**
Substitute A, D, and P into the total share equation:
\[ (5k + 5) + (4k + 10) + (3k + 15) = 4830 \]
Simplifying this gives:
\[ 12k + 30 = 4830 \]

6. **Solving for k:**
Now, isolate k:
\[ 12k = 4830 - 30 \]
\[ 12k = 4800 \]
\[ k = \frac{4800}{12} = 400 \]

7. **Finding Dishant's Original Share:**
Now that we have k, we can find Dishant's original share:
\[ D = 4k + 10 = 4(400) + 10 = 1600 + 10 = 1610 \]

### Final Answer:
Dishant's original share is Rs. 1610.