Question

If the difference between 58% and 76% of a number is 198, then the difference between 82% and 46% of the same number will be:

• A. 286
• B. 396
• C. 432
• D. 506

Hint:

When given percentage differences of the same number, convert the percentages to decimals and solve using linear equations.

Answer 1

The Correct Option is B

Let the number be \( x \). We are told: \[ 76% \text{ of } x - 58% \text{ of } x = 198 \Rightarrow (0.76x - 0.58x) = 198 \Rightarrow 0.18x = 198 \Rightarrow x = \frac{198}{0.18} = 1100 \] Now we calculate the difference between 82% and 46% of the same number: \[ (0.82 - 0.46)x = 0.36 \times 1100 = 396 \]