Saed allows two successive discounts of 10% and 20% on the marked price of a…

Concept: Successive discounts are multiplicative, not additive. When discounts of d1 and d2 are applied one after the other, the buyer finally pays (1 − d1)(1 − d2) of the marked price, so the single discount equivalent to them is 1 − (1 − d1)(1 − d2) of the marked price. Profit, in contrast, is always measured on the cost price: Profit % = (SP − CP) ÷ CP × 100.

Application to this ruler:

1. Net payment factor after 10% and then 20%: (1 − 0.10) × (1 − 0.20) = 0.90 × 0.80 = 0.72 of the marked price.

2. Equivalent single discount rate = 1 − 0.72 = 0.28, that is 28% of the marked price.

3. This discount is given as ₹140, so 0.28 × MP = 140, giving MP = 140 ÷ 0.28 = ₹500.

4. Selling price = 0.72 × 500 = ₹360.

5. Profit = SP − CP = 360 − 288 = ₹72.

6. Profit % = (72 ÷ 288) × 100 = 25%.

Cross-check and contrast:

• Applying the two discounts one at a time: 10% off ₹500 leaves ₹450, and 20% off ₹450 leaves ₹360. The total reduction is ₹500 − ₹360 = ₹140, which matches the single discount given in the question.

• Reverse check from the cost price: ₹288 × 1.25 = ₹360, the same selling price obtained above.

• The rate 28% is the single discount equivalent to 10% followed by 20%, but it is measured on the marked price of ₹500, whereas the profit rate is measured on the cost price of ₹288. Using one base in place of the other is the usual error in this type of question.

Hence Saed makes a profit of 25% on the ruler.