Aptitude · Lesson 2 of 9
Profit, loss & discount
Cost price, selling price, marked price and discount calculations.
- CP = cost price, SP = selling price, MP = marked (list) price.
- Profit = SP − CP; Profit % =
Profit / CP × 100(always on CP). - SP = CP × (1 + profit%/100); SP = CP × (1 − loss%/100).
- Discount is on MP: SP = MP × (1 − discount%/100).
- Successive discounts a% and b% equal a single discount of
a + b − ab/100. - Selling two items at the same SP, one at x% profit and one at x% loss, always gives a loss of
x²/100%.
Example: A laptop bought for ₹40,000 is sold for ₹46,000. Find the profit percent.
- Profit = 46,000 − 40,000 = ₹6,000.
- Profit % = 6,000 / 40,000 × 100.
Answer: 15%
Example: A shop marks a phone at ₹20,000 and gives successive discounts of 10% and 5%. What does the customer pay?
- Single equivalent discount = 10 + 5 − 50/100 = 14.5%.
- SP = 20,000 × (1 − 0.145) = 20,000 × 0.855.
Answer: ₹17,100
Key points
- Profit/loss % is on cost price.
- Discount % is on marked price.
- Same SP, x% gain and x% loss → x²/100 % loss overall.
Quick check
Two discounts of 20% and 10% equal a single discount of…
20 + 10 − (20 × 10)/100 = 28%.
Practice task
A trader marks goods 40% above cost and gives a 25% discount. Find his profit or loss percent.
Show answer
Take CP = 100 → MP = 140 → SP = 140 × 0.75 = 105. Profit = 5%.
Interview corner
If CP of 12 items equals SP of 10 items, what is the profit %?
Let each CP = 1: CP of 10 items = 10, SP of 10 items = 12. Profit = 2/10 × 100 = 20%.
Is a 10% markup followed by a 10% discount break-even?
No: 100 → 110 → 99, a 1% loss.
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