A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is ?

Options

A. A) 64
B. B) 76
C. C) 84
D. D) 98

Answer

To solve the problem of dividing Rs. 427 among A, B, and C such that 3 times A's share, 4 times B's share, and 7 times C's share are all equal, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the shares of A, B, and C be represented as:
- A's share = \( \frac{K}{3} \)
- B's share = \( \frac{K}{4} \)
- C's share = \( \frac{K}{7} \)

2. **Set Up the Equation**:
According to the problem, the total sum of their shares must equal Rs. 427. Therefore, we can write the equation:
\[ \frac{K}{3} + \frac{K}{4} + \frac{K}{7} = 427 \]

3. **Find a Common Denominator**:
The least common multiple (LCM) of the denominators 3, 4, and 7 is 84. We will rewrite each term with this common denominator:
\[ \frac{28K}{84} + \frac{21K}{84} + \frac{12K}{84} = 427 \]

4. **Combine the Terms**:
Combine the fractions:
\[ \frac{28K + 21K + 12K}{84} = 427 \]
This simplifies to:
\[ \frac{61K}{84} = 427 \]

5. **Solve for K**:
To isolate K, multiply both sides by 84:
\[ 61K = 427 \times 84 \]
Now calculate \( 427 \times 84 \):
\[ 427 \times 84 = 35868 \]
Now divide by 61:
\[ K = \frac{35868}{61} = 588 \]

6. **Find C's Share**:
Now that we have K, we can find C's share:
\[ C's \, share = \frac{K}{7} = \frac{588}{7} = 84 \]

### Final Answer:
The share of C is Rs. 84.

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