In an examination, Ramesh was asked to find `(3)/(14)` of a certain number. By mistake, he found `(3)/(4)` of that number. His answer was 50 more than the correct answer. The number is __________.

Options

A. `93(1)/(3)`
B. `93(1)/(7)`
C. `95(1)/(3)`
D. `95(1)/(5)`

Answer

To solve the problem step by step, let's denote the certain number as \( x \).

1. **Identify the correct and incorrect calculations**:
- Ramesh was supposed to find \( \frac{3}{14} \) of \( x \).
- Instead, he found \( \frac{3}{4} \) of \( x \).

2. **Set up the equations**:
- The correct answer (what he was supposed to find) is:
\[ \text{Correct Answer} = \frac{3}{14} x \]
- The incorrect answer (what he actually found) is:
\[ \text{Incorrect Answer} = \frac{3}{4} x \]
- According to the problem, the incorrect answer is 50 more than the correct answer:
\[ \frac{3}{4} x = \frac{3}{14} x + 50 \]

3. **Eliminate the fractions**:
- To eliminate the fractions, we can multiply the entire equation by 28 (the least common multiple of 4 and 14):
\[ 28 \cdot \left(\frac{3}{4} x\right) = 28 \cdot \left(\frac{3}{14} x + 50\right) \]
- This simplifies to:
\[ 21x = 6x + 1400 \]

4. **Rearranging the equation**:
- Now, we can rearrange the equation to isolate \( x \):
\[ 21x - 6x = 1400 \]
\[ 15x = 1400 \]

5. **Solving for \( x \)**:
- Divide both sides by 15:
\[ x = \frac{1400}{15} \]
- Simplifying \( \frac{1400}{15} \):
\[ x = \frac{280}{3} \quad \text{(which is equal to } 93 \frac{1}{3} \text{)} \]

Thus, the number is \( 93 \frac{1}{3} \).