The salary of a worker is first increased by 25%, then it is decreased by 12%. The percentage change in his salary is:

Correct — B. Successive percentage changes multiply. They do not add.

Start the salary at 100.
After +25%: 100 × 1.25 = 125
After −12%: 125 × 0.88 = 110

Net change = 110 − 100 = +10 on a base of 100 = 10% increase → option (b).

Same thing by formula: 25 − 12 − (25 × 12)⁄100 = 13 − 3 = +10%.

Why the others are wrong

• (a)
  10% decrease — Option (a) has the right size and the wrong direction. The 12% cut is taken on 125 and is worth 15, against a rise worth 25 — so the salary finishes above where it began, not below.
• (c)
  13% increase — 13% is 25 − 12, the answer from adding the percentages. It drops the cross term: the 12% is charged on 125, not on 100, which costs an extra 3 and pulls the net down to 10%.
• (d)
  13% decrease — Option (d) adds the percentages and flips the sign — 12 − 25 = −13. The rise of 25 outweighs the cut of 15 (12% of 125), so the net movement is upward.

A percentage change is a multiplier, not a quantity you can add. A rise of 25% is × 1.25 and a fall of 12% is × 0.88, so two changes in sequence multiply: 1.25 × 0.88 = 1.10.

Addition fails because of the base. The second percentage is charged on the already-changed figure, so 12% of 125 costs 15 rather than 12.

The algebraic form of the same fact is a + b + ab⁄100, taking b as negative for a fall.

Key facts

• Successive changes of a% and b% combine to a + b + ab⁄100 percent.
• A 25% rise followed by a 12% fall is a net 10% rise, because 1.25 × 0.88 = 1.10.
• A rise of x% followed by a fall of x% always leaves a net loss of x²⁄100 percent.

Common traps

• Adding 25 and −12 to get 13%.
• Applying the 12% cut to the original salary instead of the raised one.
• Assuming a rise and an equal fall cancel out.

No directly related past PYQ was found.