Profit and Loss

Why This Chapter Matters

Profit & Loss builds directly on Percentage (profit% and loss% are just percentage changes applied to Cost Price) and appears in 3-5 questions across every banking exam, often layered with successive discounts or false-weight scenarios.

Analogy — Think of Cost Price as the "starting point" a percentage change is always measured against, exactly like Original Price in a percentage-change problem. Profit% = (Profit/CP) × 100 is literally the same formula shape as "% increase = (increase/original) × 100" from Percentage — the shopkeeper's CP plays the role of "original," and Profit plays the role of "increase." Once you see Profit & Loss as Percentage applied to buying and selling, the formulas stop being a new set to memorize.

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%.

Revision Notes

Profit% = (SP-CP)/CP x 100
Loss% = (CP-SP)/CP x 100

SP = CP(100+P%)/100 or CP(100-L%)/100
CP = SP x 100/(100+P%) or SP x 100/(100-L%)

DISCOUNT: SP = MP x (100-d%)/100
SUCCESSIVE DISCOUNTS d1, d2:
Net% = d1+d2-d1xd2/100

FALSE WEIGHT PROFIT% = (True-False)/False x 100

## Try It (2 Minutes)

A shopkeeper uses a false weight of 900g instead of 1kg while buying and selling at the marked (no-discount) price. Before calculating, reason through why this alone creates profit even with "no markup": the shopkeeper pays for 900g but sells it labeled as 1000g, so for every claimed kg sold, they've actually only given away 900g of goods. Using the formula: Profit% = (1000-900)/900 × 100 ≈ 11.1% — pure profit from the weight discrepancy alone, before any price markup is even applied.