A number was mistakenly increased by 25% instead of decreased by 20%. By what percent is the final result more than the CORRECT value?

Correct — A.
Take the number as 100.

Correct value, decreased by 20% = 100 × 0.8 = 80
Wrong value, increased by 25% = 100 × 1.25 = 125
Excess = 125 − 80 = 45

Excess as a percent of the correct value = 45 ⁄ 80 × 100
= 56.25% → option (a)

Why the others are wrong

• (b)
  50.5% — 50.5% fits none of the three possible bases. The excess of 45 is 56.25% of the correct 80, 45% of the original 100 and 36% of the wrong 125.
• (c)
  45% — 45% measures the excess against the original 100. The question asks how much more than the correct value, and that is 80, not 100.
• (d)
  60.25% — 60.25% would need an excess of 48.2 on the correct value of 80. The real excess is 125 − 80 = 45, which is 56.25% of 80.

"More than X" puts X in the denominator. The stem asks how much the final result exceeds the CORRECT value, so the correct value, 80, is the base.

In multipliers: final ⁄ correct = 1.25 ⁄ 0.8 = 1.5625. That is 56.25% above 1.

The original number cancels, which is why taking it as 100 is safe.

Key facts

• Percent more than X = (difference ⁄ X) × 100
• A 20% decrease multiplies by 0.8, and a 25% increase by 1.25
• 1.25 ⁄ 0.8 = 1.5625, so the final result is 156.25% of the correct value
• 0.8 × 1.25 = 1: a 25% increase exactly undoes a 20% decrease

Common traps

• Dividing the excess by the original 100 and answering 45%
• Dividing by the wrong result 125 instead of the correct value 80

No directly related past PYQ was found.