In an examination a student was asked to find `5/17` of a certain number. By mistake he found `17/5` of that number. If his answer was `264/119` more than the correct answer then find the number.

Options

A. `7/5`
B. `5/7`
C. `3/7`
D. `7/3`

Answer

To solve the problem step by step, we will define the unknown number as \( x \).

### Step 1: Define the expressions
The student was supposed to find \( \frac{5}{17} \) of \( x \), but he mistakenly found \( \frac{17}{5} \) of \( x \).

### Step 2: Write the equations
The correct answer (what the student was supposed to find) is:
\[ \text{Correct Answer} = \frac{5}{17} x \]
The incorrect answer (what the student found) is:
\[ \text{Incorrect Answer} = \frac{17}{5} x \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the incorrect answer is \( \frac{264}{119} \) more than the correct answer. Therefore, we can write:
\[ \frac{17}{5} x = \frac{5}{17} x + \frac{264}{119} \]

### Step 4: Eliminate the fractions
To eliminate the fractions, we can multiply through by \( 85 \) (the least common multiple of the denominators 5 and 17):
\[ 85 \cdot \frac{17}{5} x = 85 \cdot \frac{5}{17} x + 85 \cdot \frac{264}{119} \]
This simplifies to:
\[ 289x = 25x + 60 \]
where \( 85 \cdot \frac{264}{119} = 60 \) (after calculating).

### Step 5: Solve for \( x \)
Now we can isolate \( x \):
\[ 289x - 25x = 60 \]
\[ 264x = 60 \]
\[ x = \frac{60}{264} \]
\[ x = \frac{5}{22} \]

### Step 6: Simplify the fraction
To simplify \( \frac{60}{264} \):
\[ x = \frac{5}{22} \]

### Final Answer
The number is \( \frac{5}{22} \).

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