Introduction to Profit and Loss

Profit and Loss

Cost Price (CP) is the price at which an article is bought. Selling Price (SP) is the price at which it is sold. Marked Price (MP) is the tag price before any discount.

• If SP > CP there is a profit: Profit = SP − CP
• If CP > SP there is a loss: Loss = CP − SP

Key formulas

• Profit % = (Profit / CP) × 100 (always on CP)
• Loss % = (Loss / CP) × 100
• SP = CP × (100 + Profit%) / 100
• SP = CP × (100 − Loss%) / 100
• Discount = MP − SP; Discount % = (Discount / MP) × 100 (on MP)
• Successive discounts a% and b%: single discount = a + b − (a × b)/100

Worked example

Bought for ₹400, sold for ₹500. Profit = ₹100, Profit % = 100/400 × 100 = 25%.

If the CP of 12 pens = SP of 10 pens: profit % = (12 − 10)/10 × 100 = 20%.

Exam tips (RRB NTPC)

• Profit/loss % is always on CP; discount % is always on MP.
• Use fractions: 25% = 1/4, 20% = 1/5, 12.5% = 1/8.
• 'CP of x items = SP of y items' → profit % = (x − y)/y × 100.

Analogy

Think of a chaiwala at a railway station. He spends ₹8 on milk, tea leaves and sugar for one cup — his cost price. He sells the cup for ₹10 — his selling price. The ₹2 he keeps is his profit, and comparing it with what he spent gives profit % = 2/8 × 100 = 25%.

On a rainy day he sells leftover tea at ₹6 a cup and loses ₹2 per cup — a loss of 25%. If his board says ₹12 but he gives a ₹2 "festival discount", that discount is counted on the board price (the marked price), not on what he spent.