A sum of Rs.2,236 is divided among A, B and C such that A receives 25% more than C and C receives 25% less than B. What is A's share in the amount?

Options

A. 1. Rs.1280
B. 2. Rs.780
C. 3. Rs.890
D. 4. Rs.460

Answer

To solve the problem, we need to find A's share from the total amount of Rs. 2,236, given the relationships between the shares of A, B, and C.

### Step-by-Step Solution:

1. **Assume B's Share**:
Let B's share be \( X \).

2. **Calculate C's Share**:
Since C receives 25% less than B, we can express C's share as:
\[ C = X - 0.25X = 0.75X = \frac{3X}{4} \]

3. **Calculate A's Share**:
A receives 25% more than C. Therefore, A's share can be calculated as:
\[ A = C + 0.25C = 1.25C = 1.25 \times \frac{3X}{4} = \frac{3X}{4} + \frac{3X}{16} \]
To combine these fractions, we need a common denominator:
\[ A = \frac{3X}{4} + \frac{3X}{16} = \frac{12X}{16} + \frac{3X}{16} = \frac{15X}{16} \]

4. **Set Up the Total Amount Equation**:
The total amount shared among A, B, and C is Rs. 2,236. Therefore, we can write:
\[ A + B + C = 2236 \]
Substituting the values we found:
\[ \frac{15X}{16} + X + \frac{3X}{4} = 2236 \]

5. **Convert All Terms to a Common Denominator**:
The common denominator for the fractions is 16. We rewrite the equation:
\[ \frac{15X}{16} + \frac{16X}{16} + \frac{12X}{16} = 2236 \]
Combining the fractions gives:
\[ \frac{15X + 16X + 12X}{16} = 2236 \]
Simplifying the numerator:
\[ \frac{43X}{16} = 2236 \]

6. **Solve for X**:
To isolate \( X \), multiply both sides by 16:
\[ 43X = 2236 \times 16 \]
Calculating the right side:
\[ 43X = 35776 \]
Now, divide by 43:
\[ X = \frac{35776}{43} = 832 \]

7. **Calculate A's Share**:
Now that we have \( X \), we can find A's share:
\[ A = \frac{15X}{16} = \frac{15 \times 832}{16} \]
Simplifying:
\[ A = \frac{12480}{16} = 780 \]

### Final Answer:
A's share in the amount is Rs. 780.