The cost of tomatoes per kg is increased by 300%. A housewife reduces her consumption of tomatoes by 70%. By what percentage does her expenditure on tomatoes increase or decrease?

Correct — B. Take 100 as the starting price per kg and 100 as the starting consumption.

Price up by 300%: new price = 100 + 300 = 400
Consumption down by 70%: new quantity = 100 − 70 = 30

Old expenditure = 100 × 100 = 10,000
New expenditure = 400 × 30 = 12,000

Change = 12,000 − 10,000 = 2,000, taken on 10,000
= 2,000 ⁄ 10,000 × 100 = an increase of 20% → option (b)

Why the others are wrong

• (a)
  Decreases, 30% — The direction is wrong before the number is. A price rising four-fold against consumption falling to 0.30 leaves 4 × 0.30 = 1.2, which is above 1, so the bill rises.
• (c)
  Decreases, 20% — The 20% is right and the direction is not. A multiplier of 1.2 makes the new expenditure 120% of the old — an increase of 20%, not a fall of 20%.
• (d)
  Increases, 30% — A 30% rise needs a multiplier of 1.3, which would require consumption at 32.5% of the old level. The question cuts it to 30%, giving 1.2.

A rise of 300% is not a rise to 300%. The new price is 100% + 300% = 400% of the old, i.e. four times it. That single reading decides the question.

Expenditure = price × quantity, so the two changes multiply rather than add: 4.00 × 0.30 = 1.20.

A multiplier above 1 is an increase and below 1 a decrease, and the size of the change is (multiplier − 1) × 100 — here 20%.

Key facts

• An increase of 300% multiplies a quantity by 4, because 100% + 300% = 400%.
• A reduction of 70% leaves a multiplier of 0.30.
• Expenditure multiplier = 4 × 0.30 = 1.20, so expenditure rises by 20%.

Common traps

• Reading 'increased by 300%' as a price of three times the old, which yields a 10% fall.
• Subtracting 70 from 300 and reaching for a bare 30%.
• Getting 20% right and then picking the option that says it decreases.

No directly related past PYQ was found.