If the selling price of Rs.36 results in a discount of 25% on the marked price…

Concept

A discount is always reckoned on the marked price, never on the selling price. If the marked price is M and the discount rate is d, the selling price is S = M x (1 - d).

The marked price is the fixed reference in such an item, so one known (discount rate, price) pair determines M, and M in turn determines the price at any other discount rate.

Application

1. A discount of 25% leaves a multiplier of 1 - 0.25 = 0.75, and that multiplier produces the given price of Rs. 36, so 0.75 x M = 36.

2. Solving for the marked price: M = 36 / 0.75 = Rs. 48.

3. A discount of 20% leaves a multiplier of 1 - 0.20 = 0.80.

4. Applying that multiplier to the marked price: 0.80 x 48 = Rs. 38.4.

Cross-check

• Direct check: 20% of Rs. 48 is Rs. 9.60, and 48 - 9.60 = Rs. 38.4.

• Second method, without computing the marked price: the two selling prices are in the ratio of their multipliers, 0.80 : 0.75 = 16 : 15, so the required price is 36 x 16/15 = Rs. 38.4.

• Common slip: adding 5% of the Rs. 36 selling price (Rs. 1.80) gives Rs. 37.8. The 5-percentage-point change in the discount rate acts on the marked price (5% of Rs. 48 = Rs. 2.40), not on the selling price.

The item should therefore be sold at Rs. 38.4.