A student was asked to multiply a given number by `(8)/(17)` . Instead, he divided the given number by `(8)/(17)` . His answer was 225 more than the correct answer. The given number was

Options

A. 64
B. 289
C. 136
D. 225

Answer

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

### Step 1: Define the correct and incorrect operations
The student was supposed to multiply the number \( X \) by \( \frac{8}{17} \). The correct answer would then be:
\[ \text{Correct Answer} = X \times \frac{8}{17} \]

However, the student mistakenly divided the number \( X \) by \( \frac{8}{17} \). The incorrect answer would be:
\[ \text{Incorrect Answer} = X \div \frac{8}{17} = X \times \frac{17}{8} \]

### Step 2: Set up the equation based on the problem statement
According to the problem, the incorrect answer was 225 more than the correct answer. Therefore, we can write the equation:
\[ X \times \frac{17}{8} = X \times \frac{8}{17} + 225 \]

### Step 3: Simplify the equation
To eliminate the fractions, we can multiply the entire equation by \( 136 \) (which is the least common multiple of 8 and 17):
\[ 136 \left( X \times \frac{17}{8} \right) = 136 \left( X \times \frac{8}{17} + 225 \right) \]

This simplifies to:
\[ 17 \times 17X = 8 \times 8X + 136 \times 225 \]
\[ 289X = 64X + 30600 \]

### Step 4: Isolate \( X \)
Now, we can isolate \( X \) by moving \( 64X \) to the left side:
\[ 289X - 64X = 30600 \]
\[ 225X = 30600 \]

### Step 5: Solve for \( X \)
Now, divide both sides by 225 to find \( X \):
\[ X = \frac{30600}{225} \]
\[ X = 136 \]

### Conclusion
The given number is \( 136 \).

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