Two successive percentage decrease of 25% each is by what percentage less than two successive percentage increase of 25% each? (Round to two decimal places.)

Correct — B. Start from 100 and run each chain.

Two decreases of 25%: 100 → 75 → 56.25, a net fall of 43.75%
Two increases of 25%: 100 → 125 → 156.25, a net rise of 56.25%

The two net figures are being compared, and less than fixes the base as the larger one, 56.25.

(56.25 − 43.75) ⁄ 56.25 × 100
= 12.5 ⁄ 56.25 × 100 = 22.22% → option (b).

Why the others are wrong

• (a)
  50% — 50% measures the 12.5-point gap against the 25% printed in the stem, since 12.5 ⁄ 25 = 50%. The base has to be the 56.25% the fall is being compared with.
• (c)
  43.75% — 43.75% is the net fall itself, 100 down to 56.25 after two cuts of 25%. It answers how far the value drops, not how that drop compares with the rise.
• (d)
  56.25% — 56.25% is the net rise, 100 up to 156.25, and it is also the value left after the two cuts. It is a figure inside the working, not the comparison asked for.

Successive percentage changes multiply, they do not add. Two falls of 25% leave 0.75 × 0.75 = 0.5625 of the value, a net fall of 43.75%, while two rises leave 1.25 × 1.25 = 1.5625, a net rise of 56.25%.

The second step is the comparison. X is p% less than Y means p = (Y − X) ⁄ Y × 100, so whatever follows less than is the base — here the 56.25% rise, not the 25% in the stem.

Key facts

• Two successive falls of 25% give a multiplier of 0.5625, which is a net fall of 43.75%.
• Two successive rises of 25% give a multiplier of 1.5625, which is a net rise of 56.25%.
• The single-step formula for two changes is a + b + ab⁄100, giving −43.75 for a = b = −25 and +56.25 for a = b = +25.
• X is p% less than Y means p = (Y − X) ⁄ Y × 100, so Y is always the base.

Common traps

• Subtracting the two net figures and answering 12.5.
• Taking 43.75 as the base instead of 56.25, which returns 28.57%.
• Assuming a 25% fall and a 25% rise cancel out.

No directly related past PYQ was found.