2.4 Marked Price and Discount

Discount is the reduction offered on the Marked Price to arrive at the Selling Price.

Discount = MP − SP Discount% = (Discount / MP) × 100 SP = MP × (100 − d)/100, where d = discount% MP = SP × 100/(100 − d)

Note carefully: discount percentage is always calculated on Marked Price, never on Cost Price. This is a frequent point of confusion — profit/loss% uses CP as base, discount% uses MP as base.

Worked Example 7: A shirt with marked price Rs 1200 is sold after a discount of 20%. Find the selling price.

Solution: SP = 1200 × 80/100 = Rs 960.

Worked Example 8: An article with marked price Rs 560 is sold for Rs 476. Find the discount percentage.

Solution: Discount = 560 − 476 = 84. Discount% = (84/560) × 100 = 15%.

Worked Example 9: After allowing a discount of 15%, an article is sold for Rs 476. Find its marked price.

Solution: MP = 476 × 100/85 = Rs 560.

Worked Example 9A (fractional discount%): A shopkeeper marks an article at Rs 800 and allows a discount of 12.5%. Find the selling price.

Solution: 12.5% = 1/8, so it is often faster to work with the fraction directly: SP = 800 − (800/8) = 800 − 100 = Rs 700. (Cross-check using the decimal form: 800 × 0.875 = 700 ✓.) Recognising standard fraction equivalents — 12.5% = 1/8, 33.33% = 1/3, 6.25% = 1/16, and so on, from the Percentage chapter — is often faster than multiplying decimals, especially for discount and markup percentages that examiners frequently choose from this list.

Worked Example 9B (reverse — from discount amount to MP): A discount of Rs 150 is allowed on the marked price of an article, and this discount is equivalent to 12% of the marked price. Find the marked price and the selling price.

Solution: Discount% = (Discount/MP) × 100 ⇒ 12 = (150/MP) × 100 ⇒ MP = 150 × 100/12 = Rs 1250. SP = MP − Discount = 1250 − 150 = Rs 1100. This is the reverse direction of the standard discount formula — here the discount amount and percentage are both given, and MP is the unknown, unlike Worked Examples 8–9 where MP or SP was already known.

Worked Example 9C (discount expressed as a fraction of MP): An article marked at Rs 3600 is sold at a discount equal to 3/8 of its marked price. Find the discount percentage and the selling price.

Solution: Discount = (3/8) × 3600 = Rs 1350. Discount% = (3/8) × 100 = 37.5%. SP = 3600 − 1350 = Rs 2250. As in Worked Example 9A, converting the fraction 3/8 directly to 37.5% (rather than first finding the discount and only then computing a percentage) saves a step.