Math · Aptitude · Chapter 03

💰 Profit & Loss

CP, SP, MP — discounts, markups, real shopkeeper math.

💡 The Three Prices

Every profit/loss question revolves around 3 numbers:

• CP — Cost Price — what the seller paid
• SP — Selling Price — what the customer paid
• MP — Marked Price — the listed/tag price (before discount)

Profit

Profit = SP − CP (when SP > CP)

Loss

Loss = CP − SP (when CP > SP)

Profit %

P% = (Profit / CP) × 100

Loss %

L% = (Loss / CP) × 100

SP from CP & P%

SP = CP × (100 + P%)/100

CP from SP & P%

CP = SP × 100/(100 + P%)

Discount

SP = MP × (100 − D%)/100

Discount %

D% = (MP − SP)/MP × 100

Important rule: Profit% and Loss% are always calculated on CP, NOT on SP. Many students make this mistake.

⚡ Shortcut: SP using multiplying factor

To find SP when there's a profit of 25%, just multiply CP by 1.25. For 30% loss, multiply CP by 0.70.

CP = ₹400, profit 25% → SP = 400 × 1.25 = ₹500. Done in seconds.

⚡ Successive discounts (tricky question type)

Item has discount 20% then another 10%. Net discount is NOT 30%.
Use: Net % = a + b − (ab/100) for discounts.
20 + 10 − (200/100) = 28% discount only.

Equivalently: SP = MP × 0.80 × 0.90 = MP × 0.72. So you pay 72%, meaning discount = 28%.

⚠️ Classic trap

"A man sells two items for ₹990 each. One at 10% profit, other at 10% loss. What's his net result?"

Instinct says "no change". Wrong. When equal SPs with equal P% and L%, there's always a net loss of (common%)²/100. Here: 100/100 = 1% loss.

🎬

Shop Visualization

Animation

When SP > CP, you make profit. When SP < CP, it's a loss. The bar length shows the difference.

🧮

Profit / Loss / Discount Calculators

Calculator

🧮 Basic P/L

CP ₹ · SP ₹

Profit ₹100 = 25%

🏷️ Discount

MP ₹ · Discount %

SP = ₹800 · You save ₹200

🔀 Two successive discounts

First % then %

Net discount: 28% (using a + b − ab/100)

Practice (SSC): A shopkeeper marks his goods 40% above cost price and gives a discount of 25%. Find his profit %.

Let CP = 100. MP = 100 × 1.40 = 140. SP = 140 × 0.75 = 105. Profit = 105 − 100 = 5. Profit% = 5/100 × 100 = 5%.

Practice (Banking): A man sells 2 articles at ₹999 each. On one he gains 11% and on the other he loses 11%. Find net result.

When equal SPs with equal +x% and −x%, there's always a loss = x²/100. Here x = 11, so loss = 121/100 = 1.21% loss. Calculate actual amounts: CP₁ = 999/1.11 = 900, CP₂ = 999/0.89 ≈ 1122.47. Total CP ≈ 2022.47, SP = 1998. Loss = 24.47, ≈ 1.21%.