Single correct option
A shopkeeper marks an article 40% above its cost price and then allows two successive discounts of 10% and 15% on the marked price. His profit percentage is
- A. 7.1%
- B. 15%
- C. 8.5%
- D. 6.4%
Show answer and solution
Answer: (A) 7.1%
Take CP = 100. Marked price = 140. After a 10% discount: 140 × 0.9 = 126. After a further 15% discount: 126 × 0.85 = 107.1.
Profit = 107.1 − 100 = 7.1, i.e. 7.1%.
Why not 15%? Successive discounts are not additive: 10% then 15% is a single discount of 1 − 0.9 × 0.85 = 23.5%, not 25%. So the net multiplier is 1.4 × 0.765 = 1.071.
Tip: Chain the multipliers (1.4 × 0.9 × 0.85) instead of adding or subtracting percentages.
Profit = 107.1 − 100 = 7.1, i.e. 7.1%.
Why not 15%? Successive discounts are not additive: 10% then 15% is a single discount of 1 − 0.9 × 0.85 = 23.5%, not 25%. So the net multiplier is 1.4 × 0.765 = 1.071.
Tip: Chain the multipliers (1.4 × 0.9 × 0.85) instead of adding or subtracting percentages.
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