Profit and Loss
Core Concepts
1. Basic Terms
Cost Price (CP): price at which article is bought.
Selling Price (SP): price at which article is sold.
Profit = SP - CP (if SP > CP).
Loss = CP - SP (if CP > SP).
Profit% = (Profit/CP) x 100.
Loss% = (Loss/CP) x 100.
2. SP from CP
SP = CP x (100 + Profit%)/100
SP = CP x (100 - Loss%)/100
3. CP from SP
CP = SP x 100/(100 + Profit%) when profit
CP = SP x 100/(100 - Loss%) when loss
4. Marked Price and Discount
Marked Price (MP) = Listed price / sticker price.
Discount = MP - SP.
Discount% = (Discount/MP) x 100.
SP = MP x (100 - Discount%)/100.
5. Successive Discounts
Two discounts d1% and d2%:
Net discount = d1 + d2 - d1xd2/100 (%)
Effective SP = MP x (1 - d1/100) x (1 - d2/100).
6. False Weight Trick
Shopkeeper uses false weight, professes to sell at CP.
Profit% = (True weight - False weight)/False weight x 100.
Practice Problems
Q1: CP=500, SP=600. Profit%? -> (100/500)x100 = 20%.
Q2: CP=800, Loss%=15%. SP? -> SP = 800 x 85/100 = 680.
Q3: SP=810, Profit%=8%. CP? -> CP = 810 x 100/108 = 750.
Q4: MP=1000, two discounts 20% and 10%. Final SP?
SP = 1000 x 0.8 x 0.9 = 720.
Net discount = 20+10-2 = 28%.
Previous Year Questions
SBI PO 2023: A man buys 8 pens for Rs 9 and sells 9 pens for Rs 8. Profit or loss%?
CP of 1 pen = 9/8. SP of 1 pen = 8/9.
Profit/Loss per pen = 8/9 - 9/8 = (64-81)/72 = -17/72 (loss).
Loss% = (17/72)/(9/8) x 100 = (17/72 x 8/9) x 100 = (136/648) x 100 = 20.99% ≈ 21% loss.
IBPS 2022: Profit on selling 10 articles = SP of 2 articles. Profit%?
Let SP of 1 article = x. Profit = 2x. CP of 10 articles = 10x - 2x = 8x. CP per article = 0.8x.
Profit% = (x - 0.8x)/0.8x x 100 = 0.2/0.8 x 100 = 25%.