Profit, Loss and Discount: Formulas in One Place

Profit and loss questions use a handful of formulas. Learn them once and apply them everywhere.

Key terms

Term	Meaning
CP	cost price, what the seller paid
SP	selling price, what the seller received
MP	marked price, the listed price
Discount	reduction on the marked price

Core formulas

• Profit = SP − CP (when SP > CP)
• Loss = CP − SP (when CP > SP)
• Profit % = (Profit ÷ CP) × 100
• Loss % = (Loss ÷ CP) × 100
• SP = CP × (100 + Profit%) ÷ 100
• CP = SP × 100 ÷ (100 + Profit%)

Profit and loss percentages are always calculated on cost price, unless stated otherwise.

Example 1: profit

CP = 400, profit 25%. SP = 400 × 125 ÷ 100 = 500.

Example 2: loss

SP = 720, loss 10%. CP = 720 × 100 ÷ 90 = 800.

Discount

• Discount = MP − SP
• Discount % = (Discount ÷ MP) × 100
• SP = MP × (100 − Discount%) ÷ 100

Example: MP = 1000, discount 20%. SP = 800.

Successive discounts

Two discounts of a% and b% are equal to a single discount of a + b − ab/100.

• 20% and 10%: 20 + 10 − 2 = 28%.
• 10% and 10%: 10 + 10 − 1 = 19%.

Finding the marked price

To make a 20% profit after giving a 10% discount on a cost of 500:

1. Required SP = 500 × 1.20 = 600.
2. SP = 90% of MP, so MP = 600 ÷ 0.9 ≈ 666.67.

Common traps

1. Wrong base. Profit is on CP; discount is on MP.
2. Adding discounts. 20% and 10% is not 30%.
3. Confusing profit% with markup. Read the wording.

Tips

• Write CP, SP and MP at the start of each problem.
• Use multipliers: 25% profit means multiply by 1.25.
• Check that a profit gives SP > CP.

Practice

Do a few of these each day, focusing on setting up the formula correctly.

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