Patwari Exam · Reasoning
Profit & Loss in Reasoning
This note explains profit%, loss%, discount, and shopkeeper's-trick questions with worked examples.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Profit/loss basics
- Profit = selling price (SP) − cost price (CP); loss = CP − SP.
- Profit%/loss% formula
- Profit% = (profit/CP) × 100; loss% = (loss/CP) × 100.
- SP/CP formula
- SP = CP × (100+profit%)/100; CP = SP × 100/(100+profit%).
- Equal-SP trick
- If 2 items are sold at the same SP, one at x% profit and the other at x% loss → overall loss = x²/100 %.
- Discount formula
- Discount: given on the marked price (MP) → SP = MP × (100−discount%)/100.
- Shopkeeper's trick
- Shopkeeper's trick: giving 800g instead of 1 kg → cheating% = (1000−800)/1000 × 100 = 20%.
- Worked example
- Exam example: CP=500, SP=600 → profit=100, profit%=20%.
Frequently Asked Questions
What is the formula for finding profit% and loss%?+
Profit% = (profit/CP) × 100 and loss% = (loss/CP) × 100, where profit = SP − CP and loss = CP − SP.
How do you find the selling price after a discount?+
Discount is given on the marked price (MP), so SP = MP × (100−discount%)/100.
How do you solve shopkeeper's-trick questions?+
For example, if a shopkeeper gives 800g instead of 1 kg, the cheating% = (1000−800)/1000 × 100 = 20%.