Profit Loss Tricks

Profit = SP – CP (SP > CP)
Loss = CP – SP (CP > SP)
Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100
SP = CP × (100 ± P/L%) ⁄ 100 (+ profit, – loss)
CP = SP × 100 ⁄ (100 ± P/L%)
Net % Profit/Loss when two articles sold at same SP & same % P/L → Always Loss % = (Common %)²⁄100

Situation	Trick
Same SP, same % P & L	“Square the % & divide by 100 → Loss”
False weight shopkeeper	Gain % = (Error ⁄ True weight) × 100
Two successive profits	Use a + b + ab⁄100 (same for loss with –ve sign)
Discount chain 10% + 20%	Single discount = 10 + 20 – (10×20)/100 = 28%

Marked Price → Discount → SP
SP = MP × (100 – D%) ⁄ 100
Profit on CP → CP = SP × 100 ⁄ (100 + P%)
False weight 900 g instead of 1 kg
Gain % = (100 g ⁄ 900 g) × 100 = 11 1⁄9 %
Article sold at x% profit, had it been sold for ₹y more, profit would be z%
CP = y × 100 ⁄ (z – x)

Q1. A shopkeeper marks 40% above CP and gives 15% discount. Net profit % is

Ans: 19%

Q2. Two articles sold at same price, one at 20% profit, other at 20% loss. Net result?

Ans: 4% loss

Q3. CP of 12 apples equals SP of 15 apples. Loss % is

Ans: 20%

Q4. After 20% discount, still 20% profit on CP. Mark-up % on CP was

Ans: 50%

Q5. 900 g sold for 1 kg. Gain % is

Ans: 11 1⁄9 %

Q6. Successive discounts 10% & 20% single equivalent discount is

Ans: 28%

Q7. SP = ₹120, Profit = 20%. CP is

Ans: ₹100

Q8. SP = ₹120, Loss = 20%. CP is

Ans: ₹150

Q9. On selling 5 pens, gain equals SP of 2 pens. Profit % is

Ans: 66 2⁄3 %

Q10. If profit doubles when SP is increased by 25%, original profit % is

Ans: 25%