Rs 33,630 are divided among A, B and C in such a manner that the ratio of the amount of A to that of B is `3 : 7` and the ratio of the amount of B to that of C Is `6 : 5`. The amount of money received by B is:

Options

A. Rs 14,868
B. Rs 16,257
C. Rs 13,290
D. Rs 12,390

Answer

To solve the problem of dividing Rs 33,630 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
The problem states that:
- The ratio of the amount of A to B is \(3:7\).
- The ratio of the amount of B to C is \(6:5\).

### Step 2: Express the Amounts in Terms of a Common Variable
Let:
- The amount received by A be \(3x\),
- The amount received by B be \(7x\) (from the first ratio),
- The amount received by B can also be expressed in terms of C. From the second ratio, let the amount received by C be \(5y\).

Since both expressions represent the amount received by B, we can equate them:
\[ 7x = 6y \]

### Step 3: Find a Common Variable
From the equation \(7x = 6y\), we can express \(y\) in terms of \(x\):
\[ y = \frac{7}{6}x \]

### Step 4: Substitute Back to Find C
Now substitute \(y\) back into the expression for C:
\[ C = 5y = 5 \left(\frac{7}{6}x\right) = \frac{35}{6}x \]

### Step 5: Calculate Total Amount
Now we can express the total amount distributed among A, B, and C:
\[ A + B + C = 3x + 7x + \frac{35}{6}x \]

To add these, we need a common denominator:
\[ A + B + C = \left(3x + 7x + \frac{35}{6}x\right) = \left(10x + \frac{35}{6}x\right) \]

Convert \(10x\) to have a denominator of 6:
\[ 10x = \frac{60}{6}x \]

Now we can combine:
\[ A + B + C = \left(\frac{60}{6}x + \frac{35}{6}x\right) = \frac{95}{6}x \]

### Step 6: Set Up the Equation
We know the total amount is Rs 33,630:
\[ \frac{95}{6}x = 33,630 \]

### Step 7: Solve for x
To find \(x\), multiply both sides by 6:
\[ 95x = 33,630 \times 6 \]
\[ 95x = 201,780 \]

Now divide by 95:
\[ x = \frac{201,780}{95} = 2,120 \]

### Step 8: Find the Amount Received by B
Now that we have \(x\), we can find the amount received by B:
\[ B = 7x = 7 \times 2,120 = 14,840 \]

### Conclusion
The amount of money received by B is **Rs 14,840**.

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