A number is increased by 20% and then decreased by 20%. What is the net change in the number?

Correct — B.
Rule: start from 100 and apply each change to the new value.

Start: 100
Increase by 20%: 100 + 20 = 120
Decrease by 20% of 120: 120 − 24 = 96

Net change: 96 − 100 = −4, a 4% decrease → option (b).

Why the others are wrong

• (a)
  4% increase — 4% increase has the right size and the wrong direction. The 20% cut is taken from 120, so it removes 24, more than the 20 that was added.
• (c)
  No change — No change assumes +20% and −20% cancel. They do not: the decrease is 20% of the larger number, 120, so it removes 24, not 20.
• (d)
  1% decrease — 1% decrease is what a 10% rise and a 10% fall give (100 → 110 → 99). With 20% each way, the loss is 20 × 20 ÷ 100 = 4%.

Successive percentage changes do not simply add, because the second change acts on a new base. For changes of x% and then y%, the net change is x + y + xy⁄100 percent, with a decrease written as negative.

Here x = 20 and y = −20: 20 − 20 − 400⁄100 = −4%. An equal rise and fall of x% always ends x²⁄100 percent below the start.

Key facts

• Net change for successive changes of x% and y%: x + y + xy⁄100.
• An equal rise and fall of x% gives a net fall of x²⁄100 percent.
• 20% of 120 is 24.

Common traps

• Assuming a 20% rise and a 20% fall cancel out
• Taking the 20% decrease from the original 100 instead of the new value 120

No directly related past PYQ was found.