Profit, Loss & Discount

Profit & Loss questions are percentage questions applied to buying and selling — the terminology is the only new thing here.

Key terms and formulas

Term	Meaning
CP	Cost Price — what the seller paid
SP	Selling Price — what the buyer pays
MP	Marked Price — the "tag" price before discount
Profit %	((SP − CP) / CP) × 100
Loss %	((CP − SP) / CP) × 100
Discount %	((MP − SP) / MP) × 100

SP = MP × (1 − Discount%/100). SP = CP × (1 + Profit%/100) or CP × (1 − Loss%/100).

Worked Example 1

UdaanPath's print partner produces an exam guide booklet for ₹800 and it's sold through the UdaanPath store for ₹1,000. Find the profit percentage.

Profit = 1000 − 800 = 200. Profit% = (200/800) × 100 = 25%.

Worked Example 2

An UdaanPath premium course marked at ₹1,200 is sold after a 15% launch-week discount. Find the selling price.

SP = 1200 × (1 − 0.15) = 1200 × 0.85 = ₹1,020.

Worked Example 3 — chained discounts

UdaanPath's Diwali sale offers successive discounts of 20% and 10% on a mock-test package marked at ₹5,000. Find the final price.

After 20%: 5000 × 0.8 = 4000. After 10%: 4000 × 0.9 = ₹3,600. (Note: this is not the same as a flat 30% discount, which would give ₹3,500.)

Common mistakes

Profit/Loss percentage is always calculated on CP, never on SP — mixing this up is the most common error in this topic.

Practice Set

1. A book bought for ₹250 is sold at a loss of 8%. Find the SP.
2. Find the single discount equivalent to two successive discounts of 10% and 20%.
3. A trader marks goods 40% above cost and allows a 25% discount. Find his profit or loss %.
4. An article is sold for ₹690 at a profit of 15%. Find the cost price.