A sum of Rs 86,700 is to be divided among A, B and C in such a manner that for every rupee that A gets B gets 90 paise and for every rupee that B gets C gets 110 paise. B's share will be:

Options

A. Rs 26,010
B. Rs 27,000
C. Rs 28,000
D. Rs 28,090

Answer

To solve the problem of dividing Rs 86,700 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Establish the Ratios
According to the problem:
- For every rupee that A gets, B gets 90 paise. This means if A gets 1 rupee, B gets 0.90 rupees.
- For every rupee that B gets, C gets 110 paise. This means if B gets 1 rupee, C gets 1.10 rupees.

### Step 2: Express B's Share in Terms of A's Share
Let A's share be represented as \( X \) rupees. Then:
- B's share = \( 0.90X \) rupees.

### Step 3: Express C's Share in Terms of B's Share
Now, since B's share is \( 0.90X \):
- C's share = \( 1.10 \times 0.90X = 0.99X \) rupees.

### Step 4: Write the Total Share in Terms of X
Now we can express the total share of A, B, and C:
- Total = A's share + B's share + C's share
- Total = \( X + 0.90X + 0.99X \)
- Total = \( (1 + 0.90 + 0.99)X = 2.89X \)

### Step 5: Set Up the Equation
We know the total amount to be distributed is Rs 86,700. Therefore, we can set up the equation:
\[ 2.89X = 86,700 \]

### Step 6: Solve for X
To find \( X \):
\[ X = \frac{86,700}{2.89} \]
Calculating this gives:
\[ X \approx 30,000 \]

### Step 7: Calculate B's Share
Now that we have A's share, we can find B's share:
\[ B's \, share = 0.90X = 0.90 \times 30,000 = 27,000 \]

### Final Answer
Thus, B's share will be **Rs 27,000**.

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