Topic A5

Financial Arithmetic & Consumer Math

Profit on CP, discount on MP — get the base right and the rest is easy.

A. Profit & Loss

Cost Price (CP)
The price at which a shopkeeper buys an item. This is always the base for profit% and loss%.
ExampleShopkeeper buys a shirt for Rs.800 → CP = Rs.800
Selling Price (SP)
The price at which the shopkeeper sells the item. Determines if it is profit or loss.
ExampleHe sells it for Rs.1000 → SP = Rs.1000
Profit
When SP is greater than CP. You made more than you paid.
FormulaProfit = SP − CP
Profit% = (Profit ÷ CP) × 100
Loss
When CP is greater than SP. You sold for less than you paid.
FormulaLoss = CP − SP
Loss% = (Loss ÷ CP) × 100
Example 1 — CP=Rs.800, SP=Rs.1000
1SP > CP → it is a profit
2Profit = 1000 − 800 = Rs.200
3Profit% = (200 ÷ 800) × 100 = 25%
Profit = Rs.200 | Profit% = 25%
Example 2 — CP=Rs.1200, Profit%=25%. Find SP.
1Profit = 25% of CP = 0.25 × 1200 = Rs.300
2SP = CP + Profit = 1200 + 300 = Rs.1500
SP = Rs.1500
Example 3 — SP=Rs.850, Loss%=15%. Find CP.
1CP = SP × 100 ÷ (100 − Loss%)
2= 850 × 100 ÷ 85 = Rs.1000
CP = Rs.1000
⚠ Always on CP: Profit% and Loss% are always calculated on Cost Price — never on SP. This is the most common MCQ trap in this topic.

B. Discount

Marked Price (MP)
The price written on the label — before any discount is applied. Discount is always calculated on MP.
ExampleLabel says Rs.2000 → MP = Rs.2000
Discount
An amount reduced from the marked price to attract buyers.
FormulaDiscount = MP − SP
Discount% = (Discount ÷ MP) × 100
SP after discount = MP × (1 − Discount%/100)
Example 1 — MP=Rs.2000, Discount=15%. Find SP.
1Discount = 15% of 2000 = 0.15 × 2000 = Rs.300
2SP = 2000 − 300 = Rs.1700
SP = Rs.1700
Example 2 — MP=Rs.800, SP=Rs.680. Find Discount%.
1Discount = MP − SP = 800 − 680 = Rs.120
2Discount% = (120 ÷ 800) × 100 = 15%
Discount% = 15%

C. Tax & Net Pay

Tax (GST / VAT)
An extra charge added on top of the price. It increases what the buyer pays.
FormulaTax = Price × Tax% ÷ 100
Final price = Price + Tax
Net Pay
The salary a worker actually takes home after deductions (taxes, pension, etc.) are removed from gross pay.
FormulaNet Pay = Gross Pay − Total Deductions
Example 1 — Price=Rs.3500, Tax=17%
1Tax = 17% of 3500 = 0.17 × 3500 = Rs.595
2Final price = 3500 + 595 = Rs.4095
Final price = Rs.4095
Example 2 — Gross=Rs.45000, Deductions=Rs.7000
1Net Pay = 45000 − 7000 = Rs.38000
Net Pay = Rs.38,000

The Price Chain — What Each % Is Based On

CP Cost Price Profit% on CP MP Marked Price Discount% on MP SP Selling Price +Tax% on SP $ Profit% and Loss% → always on CP · Discount% → always on MP · Tax → added on SP

D. Critical Rules — Don't Mix These Up

Profit% and Loss%
Always on CP
CP = what you bought it for
SP>CP → Profit   SP<CP → Loss
Discount%
Always on MP
MP = the label price
Discount reduces MP to SP
Tax
Added to Price
Makes final amount bigger
Paid by the buyer
Memory trick: Profit/Loss → Cost Price. Discount → Marked Price. C comes before M in the alphabet and in the selling chain.

Quick MCQ Revision

FormulaRemember
Profit%(Profit ÷ CP) × 100
Loss%(Loss ÷ CP) × 100
Discount%(Discount ÷ MP) × 100
SP from CP+Profit%CP × (1 + Profit%/100)
CP from SP+Profit%SP × 100 ÷ (100 + Profit%)
Key