Rs 70200 is divided among A B and C in such a way that A receive `(4)/(5)` the sum of (B+C). Find the amount received by C if B receives `(2)/(11)` the sum of `(A+C)` ?

Options

A. Rs 28200
B. Rs 29140
C. Rs 32940
D. Rs 25850

Answer

To solve the problem step by step, we will use the information provided in the question and set up equations based on the relationships between A, B, and C.

### Step 1: Define the total amount and relationships
Let the total amount be Rs 70,200. According to the problem:
- A receives \( \frac{4}{5} \) of the sum of B and C.
- B receives \( \frac{2}{11} \) of the sum of A and C.

### Step 2: Set up the equations
From the information given, we can express A in terms of B and C:
\[ A = \frac{4}{5}(B + C) \]
Also, since the total amount is Rs 70,200, we have:
\[ A + B + C = 70,200 \]

### Step 3: Express B in terms of A and C
From the second condition, we can express B in terms of A and C:
\[ B = \frac{2}{11}(A + C) \]

### Step 4: Substitute B in the total amount equation
Now, we can substitute the expression for B into the total amount equation:
\[ A + \frac{2}{11}(A + C) + C = 70,200 \]

### Step 5: Simplify the equation
Multiply through by 11 to eliminate the fraction:
\[ 11A + 2(A + C) + 11C = 11 \times 70,200 \]
This simplifies to:
\[ 11A + 2A + 2C + 11C = 772200 \]
Combining like terms gives:
\[ 13A + 13C = 772200 \]

### Step 6: Factor out common terms
Factoring out 13 from the left side:
\[ 13(A + C) = 772200 \]
Now, divide both sides by 13:
\[ A + C = \frac{772200}{13} = 59400 \]

### Step 7: Substitute back to find A
Now we can substitute \( A + C = 59400 \) back into the equation for B:
\[ B = \frac{2}{11}(A + C) = \frac{2}{11}(59400) = 10800 \]

### Step 8: Find A using the total amount
Now we can find A using the total amount:
\[ A + B + C = 70,200 \]
Substituting B:
\[ A + 10800 + C = 70200 \]
This simplifies to:
\[ A + C = 59400 \quad \text{(which we already found)} \]

### Step 9: Find C
Now, we can find C by substituting A back into the equation for A:
Using \( A = \frac{4}{5}(B + C) \):
\[ A = \frac{4}{5}(10800 + C) \]
Substituting \( A + C = 59400 \):
\[ C = 59400 - A \]

### Step 10: Solve for C
Now we can substitute \( A \) back into the equation:
1. From \( A + C = 59400 \), we can express C as:
\[ C = 59400 - A \]
2. Substitute \( A = \frac{4}{5}(10800 + C) \) into this equation and solve for C.

After solving, we find that:
\[ C = 28,200 \]

### Final Answer
Thus, the amount received by C is Rs 28,200.

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