Profit, Loss & Discount

Scenario

Blinkit shows you a '20% off' tag, but they marked up the base price by 25% first.

Are you really getting a discount, or just paying the original price?

Mental model

Cost Price (CP) is the anchor. Everything scales relative to what the seller paid.

Profit and loss are percentage increases/decreases on CP. Discount is a percentage decrease on Marked Price (MP). Three different bases — mix them and every answer is wrong.

Formula

Profit% = (Profit / CP) x 100. Loss% = (Loss / CP) x 100. Discount% = (Discount / MP) x 100. SP = MP x (1 - Discount/100). SP = CP x (1 + Profit/100). If two successive discounts a% and b%: net = a + b - ab/100.

Three bases, three formulas. Profit/Loss always on CP; Discount always on MP. To find CP from SP when profit% is known: CP = SP / (1 + Profit/100).

Pattern discovery

Compare the profit or loss against the original cost.

• CP=100, SP=120 -> Profit=20, Profit%=20%
• CP=200, SP=240 -> Profit=40, Profit%=20%
• CP=100, SP=80 -> Loss=20, Loss%=20%

What is the constant denominator used for calculating profit or loss percentage?

Rule: Cost Price (CP) is the anchor. Always calculate P/L percentage relative to what was paid originally.

Worked example

Problem: A shopkeeper marks a bag 40% above cost price and gives a 10% discount. Find the profit percentage.

1. Set up: Let CP = 100. MP = CP x 1.40 = 140.
2. Apply discount to MP: SP = 140 x (1 - 10/100) = 140 x 0.90 = 126.
3. Compute profit: Profit = SP - CP = 126 - 100 = 26.
4. Profit% = (26 / 100) x 100 = 26%.
5. Sanity-check: Markup then discount compound multiplicatively: 1.40 x 0.90 = 1.26, so 26% profit. Matches.

Answer: 26% profit.

Problem: By selling an item for Rs660, a person makes 10% loss. At what price must he sell it to make 10% profit?

1. Set up: SP = 660, Loss = 10%, so SP = CP x 0.90.
2. Find CP: CP = 660 / 0.90 = 733.33 (Rs733.33).
3. Apply 10% profit: Target SP = CP x 1.10 = 733.33 x 1.10 = 806.67.
4. Sanity-check: Rs806.67 > Rs733.33 (CP) by Rs73.33 = 10% of 733.33. Correct.

Answer: Rs806.67 (approx Rs807).

Shortcuts

• Multiplier Method: For 20% profit, SP = 1.2 x CP. For 15% loss, SP = 0.85 x CP. This skips the intermediate add/subtract step. (If CP is 400 and profit is 25%, SP = 400 x 1.25 = 500.)
• Successive Discount: Two successive discounts of a% and b% equal a single discount of (a + b - ab/100)%. (Successive discounts of 20% and 10% = 20 + 10 - (20x10/100) = 28% total discount, not 30%.)

Common mistakes

• Base Confusion: Calculating profit percentage on Selling Price instead of Cost Price. Profit of 20 on SP of 120 is a 16.67% profit, not 20%.
• Fake Net Zero: Thinking a 20% markup followed by a 20% discount brings you back to the original price. 1.2 x 0.8 = 0.96 — that's a 4% loss.

Glossary

markup

The amount added to the cost price to set the selling price.

discount

A reduction in the marked price given to a buyer.

multiplicatively

Multiplying numbers together step-by-step to find a total change.

Recall questions

• If an item is bought for Rs500 and sold for Rs600, what is the profit percentage?
• A shirt marked at Rs1000 is sold after a 15% discount. What is the selling price?
• If SP is Rs900 after a 10% loss, what was the CP?

Questions & answers

A shopkeeper marks his goods 25% above CP and allows a discount of 10%. Find his overall profit percentage.

12.5%

Approach: Let CP = 100. MP = 125. SP = 125 x 0.90 = 112.5. Profit = 12.5%.

By selling 33 metres of cloth, a person gains the selling price of 11 metres. Find the gain percentage.

50%

Approach: Let SP of 1m = 1. SP of 33m = 33. Gain = SP of 11m = 11. CP = 33 - 11 = 22. Gain% = (11/22) x 100 = 50%.

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