₹ 555 was to be divided among A, B and C in the ratio of 1/4:1/5:1/6. But by mistake it was divided in the ratio of 4:5:6. The amount in excess received by C was

Options

A. ₹ 72
B. ₹ 75
C. ₹ 22
D. ₹ 52

Answer

To solve the problem, we need to determine the excess amount received by C when ₹555 was mistakenly divided among A, B, and C in the ratio of 4:5:6 instead of the intended ratio of 1/4:1/5:1/6.

### Step-by-Step Solution:

1. **Determine the Intended Ratio**:
The intended ratio is given as \( \frac{1}{4} : \frac{1}{5} : \frac{1}{6} \).

2. **Find the LCM of the Denominators**:
To eliminate the fractions, we need to find the least common multiple (LCM) of the denominators (4, 5, and 6).
- The prime factorization is:
- 4 = \( 2^2 \)
- 5 = \( 5^1 \)
- 6 = \( 2^1 \times 3^1 \)
- The LCM is \( 2^2 \times 3^1 \times 5^1 = 60 \).

3. **Convert the Ratios**:
Multiply each term in the ratio by 60 to convert it to whole numbers:
- For \( \frac{1}{4} \): \( 60 \div 4 = 15 \)
- For \( \frac{1}{5} \): \( 60 \div 5 = 12 \)
- For \( \frac{1}{6} \): \( 60 \div 6 = 10 \)
- Thus, the intended ratio is \( 15 : 12 : 10 \).

4. **Calculate the Total Parts**:
The total parts in the intended ratio is \( 15 + 12 + 10 = 37 \).

5. **Calculate C's Intended Share**:
C's intended share from ₹555 is calculated as follows:
\[ \text{C's share} = \frac{10}{37} \times 555 = \frac{5550}{37} = 150 \]

6. **Calculate the Mistaken Ratio**:
The mistaken ratio is \( 4 : 5 : 6 \).
- The total parts in the mistaken ratio is \( 4 + 5 + 6 = 15 \).

7. **Calculate C's Mistaken Share**:
C's share in the mistaken division is:
\[ \text{C's share} = \frac{6}{15} \times 555 = \frac{3330}{15} = 222 \]

8. **Calculate the Excess Amount**:
The excess amount received by C is:
\[ \text{Excess} = \text{C's mistaken share} - \text{C's intended share} = 222 - 150 = 72 \]

### Final Answer:
The amount in excess received by C is ₹72.

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