rupes 750 is divided among A , B and C in such a manner that A : B = 5 :2 and B: C = 7: 13 How much is C's share more than B's share

Options

A. rupes 50
B. rupes 130
C. rupes 120
D. rupes 150

Answer

To solve the problem of how much C's share is more than B's share when Rs. 750 is divided among A, B, and C in the ratios A:B = 5:2 and B:C = 7:13, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Ratios**:
- The ratio of A to B is given as \( A : B = 5 : 2 \).
- The ratio of B to C is given as \( B : C = 7 : 13 \).

2. **Express Ratios in Terms of a Common Variable**:
- Let’s express A, B, and C in terms of a common variable \( x \).
- From \( A : B = 5 : 2 \), we can write:
\[ A = 5x \quad \text{and} \quad B = 2x \]
- From \( B : C = 7 : 13 \), we can express B in terms of another variable \( y \):
\[ B = 7y \quad \text{and} \quad C = 13y \]

3. **Equate the Two Expressions for B**:
- Since both expressions represent B, we can set them equal to each other:
\[ 2x = 7y \]
- From this equation, we can express \( x \) in terms of \( y \):
\[ x = \frac{7y}{2} \]

4. **Substitute x Back into A and C**:
- Now substitute \( x \) back into the expressions for A and C:
\[ A = 5x = 5 \left(\frac{7y}{2}\right) = \frac{35y}{2} \]
\[ C = 13y \]

5. **Calculate the Total Amount in Terms of y**:
- The total amount is given as Rs. 750, so we can write:
\[ A + B + C = 750 \]
- Substituting the values:
\[ \frac{35y}{2} + 7y + 13y = 750 \]
- To combine the terms, convert \( 7y \) and \( 13y \) to have a common denominator:
\[ \frac{35y}{2} + \frac{14y}{2} + \frac{26y}{2} = 750 \]
- This simplifies to:
\[ \frac{75y}{2} = 750 \]

6. **Solve for y**:
- Multiply both sides by 2:
\[ 75y = 1500 \]
- Now divide by 75:
\[ y = 20 \]

7. **Find the Values of A, B, and C**:
- Now substitute \( y \) back to find A, B, and C:
\[ B = 7y = 7 \times 20 = 140 \]
\[ C = 13y = 13 \times 20 = 260 \]

8. **Calculate the Difference Between C and B**:
- Finally, to find how much C's share is more than B's share:
\[ C - B = 260 - 140 = 120 \]

### Final Answer:
C's share is Rs. 120 more than B's share.

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