Divide Rs 1250 among A, B, C, so that A gets `2/9` of B's share and C gets `3/4` of A's share. Find the shares of A, B and C.

Options

A. Rs 200, Rs 800, Rs 250
B. Rs 200, Rs 900, Rs 150
C. Rs 20, Rs 800, Rs 300
D. Rs 200, Rs 900, Rs 75

Answer

To solve the problem of dividing Rs 1250 among A, B, and C based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationships**:
- A gets \( \frac{2}{9} \) of B's share.
- C gets \( \frac{3}{4} \) of A's share.

2. **Express A's Share in Terms of B's Share**:
- Let B's share be \( b \).
- Then A's share can be expressed as:
\[ a = \frac{2}{9}b \]

3. **Express C's Share in Terms of A's Share**:
- From the relationship given, C's share can be expressed as:
\[ c = \frac{3}{4}a \]
- Substitute \( a \) from the previous step:
\[ c = \frac{3}{4} \left( \frac{2}{9}b \right) = \frac{3 \times 2}{4 \times 9}b = \frac{6}{36}b = \frac{1}{6}b \]

4. **Set Up the Total Share Equation**:
- Now we have expressions for A, B, and C in terms of B's share:
\[ a = \frac{2}{9}b, \quad b = b, \quad c = \frac{1}{6}b \]
- The total amount shared among A, B, and C is Rs 1250:
\[ a + b + c = 1250 \]
- Substitute the expressions:
\[ \frac{2}{9}b + b + \frac{1}{6}b = 1250 \]

5. **Find a Common Denominator**:
- The common denominator for 9 and 6 is 18. Convert each term:
\[ \frac{4}{18}b + \frac{18}{18}b + \frac{3}{18}b = 1250 \]
- Combine the fractions:
\[ \frac{4 + 18 + 3}{18}b = 1250 \quad \Rightarrow \quad \frac{25}{18}b = 1250 \]

6. **Solve for B's Share**:
- Multiply both sides by \( \frac{18}{25} \):
\[ b = 1250 \times \frac{18}{25} = 1250 \times 0.72 = 900 \]

7. **Calculate A's and C's Shares**:
- Substitute \( b \) back to find \( a \) and \( c \):
\[ a = \frac{2}{9} \times 900 = 200 \]
\[ c = \frac{1}{6} \times 900 = 150 \]

8. **Final Shares**:
- A's share = Rs 200
- B's share = Rs 900
- C's share = Rs 150

### Summary of Shares:
- A = Rs 200
- B = Rs 900
- C = Rs 150