Question

The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

• A. 70
• B. 65
• C. 40
• D. 90

Hint:

Let the number be x; write 1.25x - 0.70x = 22 and solve.

Answer 1

The Correct Option is C

Instead of working with decimals directly, this can be solved using fractions, which avoids rounding and keeps the arithmetic exact.

1. Let the original number be $x$.
2. A 25% increase means the new value is $x + \frac{1}{4}x = \frac{5x}{4}$.
3. A 30% decrease means the new value is $x - \frac{3}{10}x = \frac{7x}{10}$.
4. The problem states the difference between these two values is 22:\[ \frac{5x}{4} - \frac{7x}{10} = 22 \]
5. Take the LCM of 4 and 10, which is 20, and rewrite both fractions:\[ \frac{25x}{20} - \frac{14x}{20} = 22 \]\[ \frac{11x}{20} = 22 \]
6. Solve for $x$:\[ x = \frac{22 \times 20}{11} = \frac{440}{11} = 40 \]
7. Testing back: $\frac{5}{4}\times 40 = 50$ and $\frac{7}{10}\times 40 = 28$, and $50-28=22$, which checks out.

\[\boxed{x = 40}\]