Percentage & Profit-Loss

Percentage & Profit-Loss

Concept

Percentages are just fractions dressed up to look scary. “45% of 200” just means 45 out of every 100 parts of 200 — so you’re scaling down first, then multiplying. Once that clicks, profit and loss are just additions or subtractions on top of the Cost Price (CP).

The key thing to remember: gain or loss is always calculated relative to the Cost Price, not the Selling Price (SP). This trips up a lot of students. If something costs ₹100 (CP) and you sell it for ₹120 (SP), your gain is ₹20 — which is 20% of ₹100, not of ₹120.

Now here’s where it gets more interesting: shops don’t always sell at cost. They mark up the price first (called the Marked Price or MP), then offer a discount on that. So the price a customer actually pays is MP minus the discount. The shopkeeper’s profit or loss is still measured against the original CP.

Key Formulas

Formula	Use
Percentage = (Part ÷ Whole) × 100	Convert any fraction to a %
Gain% = ((SP − CP) ÷ CP) × 100	Find profit percentage
Loss% = ((CP − SP) ÷ CP) × 100	Find loss percentage
Discount % = ((MP − SP) ÷ MP) × 100	Find discount percentage
SP with Gain = CP × (1 + Gain%)/100	Find selling price from CP and gain%
Break-even: SP = CP	No profit, no loss

Worked Example

Q: An article costs ₹800. The shopkeeper marks it up by 40% and then offers a 10% discount. What is the final selling price?

Step 1: Find Marked Price (MP = CP + 40% of CP) MP = 800 + (40 ÷ 100) × 800 = 800 + 320 = ₹1,120

Step 2: Apply 10% discount on MP Discount = (10 ÷ 100) × 1120 = ₹112 SP = MP − Discount = 1120 − 112 = ₹1,008

Answer: ₹1,008

Common Errors

• Finding gain% using SP as the base → Always use CP as the denominator: Gain% = (Gain ÷ CP) × 100
• Confusing MP with SP → MP is the listed price before discount; SP is what the customer actually pays
• Adding percentages directly when a discount follows a markup → Can’t just do 40% − 10% = 30%. You must apply them sequentially: MP = CP × 1.40, then SP = MP × 0.90