A sum of Rs. 13,725 is divided between A,B,C and D such that ratio of the shares of A and B is `3:4` ,that of B and C is `8 :5` and that of C and D is `7 :10` .What is the share of C?

Options

A. Rs. 2,625
B. Rs. 2,475
C. Rs. 3,150
D. Rs.3,750

Answer

To solve the problem, we need to find the share of C from the total sum of Rs. 13,725, given the ratios of shares among A, B, C, and D.

### Step-by-Step Solution:

1. **Identify the Ratios:**
- The ratio of A to B is \(3:4\).
- The ratio of B to C is \(8:5\).
- The ratio of C to D is \(7:10\).

2. **Express the Ratios in Terms of a Common Variable:**
- Let the share of A be \(3x\) and the share of B be \(4x\) (from the ratio \(3:4\)).
- Since B is also related to C, we can express B in terms of C. From the ratio \(B:C = 8:5\), we can express B as \(8y\) and C as \(5y\).
- Now we have two expressions for B: \(4x = 8y\). This gives us \(x = 2y\).

3. **Express C in Terms of x:**
- From \(C = 5y\) and \(x = 2y\), we can substitute \(y\) with \(x\):
\[ y = \frac{x}{2} \implies C = 5y = 5 \left(\frac{x}{2}\right) = \frac{5x}{2} \]

4. **Express D in Terms of C:**
- From the ratio \(C:D = 7:10\), we can express D as \(D = \frac{10}{7}C\).
- Substituting \(C = \frac{5x}{2}\):
\[ D = \frac{10}{7} \cdot \frac{5x}{2} = \frac{50x}{14} = \frac{25x}{7} \]

5. **Combine All Shares:**
- Now we can express the total sum of shares:
\[ A + B + C + D = 3x + 4x + \frac{5x}{2} + \frac{25x}{7} \]
- To combine these, we need a common denominator. The least common multiple of 2 and 7 is 14:
\[ A = 3x = \frac{42x}{14}, \quad B = 4x = \frac{56x}{14}, \quad C = \frac{5x}{2} = \frac{35x}{14}, \quad D = \frac{25x}{7} = \frac{50x}{14} \]
- Adding these together:
\[ A + B + C + D = \frac{42x + 56x + 35x + 50x}{14} = \frac{183x}{14} \]

6. **Set Up the Equation:**
- We know the total amount is Rs. 13,725:
\[ \frac{183x}{14} = 13725 \]

7. **Solve for x:**
- Multiply both sides by 14:
\[ 183x = 13725 \times 14 \]
- Calculate \(13725 \times 14 = 192150\):
\[ 183x = 192150 \]
- Divide by 183:
\[ x = \frac{192150}{183} = 1050 \]

8. **Find the Share of C:**
- Recall that \(C = \frac{5x}{2}\):
\[ C = \frac{5 \times 1050}{2} = \frac{5250}{2} = 2625 \]

### Final Answer:
The share of C is **Rs. 2625**.