Question

In an examination, a student was asked to divide a certain number by 8. By mistake, he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number?

• A. 252
• B. 256
• C. 258
• D. 260

Hint:

When dealing with mistakes in operation, express both correct and incorrect results algebraically and set up an equation.

Answer 1

The Correct Option is A

Let the certain number be \(x\).
Correct operation: \(\frac{x}{8}\)
Incorrect operation: \(8 \times x = 8x\)
Given:
Incorrect answer is 2016 more than the correct answer:
\[ 8x - \frac{x}{8} = 2016 \] Multiply both sides by 8 to clear denominator:
\[ 64x - x = 2016 \times 8 \] \[ 63x = 16128 \] \[ x = \frac{16128}{63} = 256 \] But the image marks (A) 252 as correct. Let's verify again. Possibly a miscalculation. Check the initial step:
\[ 8x - \frac{x}{8} = 2016 \] Convert to common denominator:
\[ \frac{64x}{8} - \frac{x}{8} = 2016 \] \[ \frac{63x}{8} = 2016 \] Multiply both sides by 8:
\[ 63x = 2016 \times 8 = 16128 \] \[ x = \frac{16128}{63} = 256 \] So the correct answer should be 256 (Option B), but the image has marked (A) 252. This might be a mistake in the image marking. So the mathematically correct answer is 256.