2430 are distributed among three persons so that their shares be diminished by 5, 10 and 15 respectively, the remainder shall be in the ratio 3:4:5. The share of C is

Options

A. रु 1015
B. रु 605
C. रु 810
D. रु 1415

Answer

To solve the problem, we need to distribute Rs. 2430 among three persons A, B, and C such that their shares are diminished by Rs. 5, Rs. 10, and Rs. 15 respectively, and the remaining amounts are in the ratio 3:4:5.

### Step-by-Step Solution:

1. **Define the Shares**:
Let the shares of A, B, and C be represented as:
- A's share = \( a \)
- B's share = \( b \)
- C's share = \( c \)

2. **Set Up the Diminished Shares**:
According to the problem, after diminishing their shares:
- A's remaining share = \( a - 5 \)
- B's remaining share = \( b - 10 \)
- C's remaining share = \( c - 15 \)

3. **Establish the Ratio**:
The remaining shares are in the ratio 3:4:5. Therefore, we can write:
\[ a - 5 : b - 10 : c - 15 = 3 : 4 : 5 \]
We can express this in terms of a variable \( x \):
\[ a - 5 = 3x, \quad b - 10 = 4x, \quad c - 15 = 5x \]

4. **Express Shares in Terms of x**:
Rearranging the equations gives us:
- \( a = 3x + 5 \)
- \( b = 4x + 10 \)
- \( c = 5x + 15 \)

5. **Total Shares**:
The total amount distributed is given as Rs. 2430. Therefore, we can write:
\[ a + b + c = 2430 \]
Substituting the expressions for \( a \), \( b \), and \( c \):
\[ (3x + 5) + (4x + 10) + (5x + 15) = 2430 \]

6. **Combine Like Terms**:
Simplifying the left side:
\[ 3x + 4x + 5x + 5 + 10 + 15 = 2430 \]
\[ 12x + 30 = 2430 \]

7. **Solve for x**:
Subtract 30 from both sides:
\[ 12x = 2430 - 30 \]
\[ 12x = 2400 \]
Now, divide by 12:
\[ x = \frac{2400}{12} = 200 \]

8. **Calculate Individual Shares**:
Now substitute \( x \) back to find \( a \), \( b \), and \( c \):
- \( a = 3(200) + 5 = 600 + 5 = 605 \)
- \( b = 4(200) + 10 = 800 + 10 = 810 \)
- \( c = 5(200) + 15 = 1000 + 15 = 1015 \)

9. **Final Answer**:
The share of C is Rs. 1015.