Profit, Loss and Discount

Overview

Profit, Loss and Discount form the backbone of commercial mathematics at the primary level. This topic tests a student's ability to apply percentage concepts to real-world buying and selling scenarios—skills essential for both daily life and competitive exams. In Bihar TET Paper I, questions from this area are straightforward but require careful attention to terminology and calculation.

The topic connects directly with percentage and ratio concepts you have already studied. Examiners typically frame questions around finding profit or loss percentage, calculating selling price when profit/loss is given, or determining the final price after applying discounts. Mastery here builds a foundation for more advanced problems in Simple Interest and Data Handling.

Students must be comfortable converting between fractions, decimals and percentages, and should practice identifying what is being asked—whether it is an absolute amount or a percentage figure. Speed and accuracy in basic arithmetic are crucial.

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Key Concepts

• **Cost Price (CP):** The price at which an article is purchased or manufactured. This is your baseline for all profit/loss calculations.

• **Selling Price (SP):** The price at which an article is sold to a customer. Compare SP with CP to determine profit or loss.

• **Profit (Gain):** When SP > CP, the seller earns a profit. Profit = SP − CP.

• **Loss:** When SP < CP, the seller incurs a loss. Loss = CP − SP.

• **Profit Percentage:** Always calculated on Cost Price. Profit% = (Profit / CP) × 100.

• **Loss Percentage:** Also calculated on Cost Price. Loss% = (Loss / CP) × 100.

• **Marked Price (MP):** The price written on the label or tag before any discount is given. Also called "list price."

• **Discount:** A reduction offered on the Marked Price. Discount = MP − SP. Discount% = (Discount / MP) × 100.

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Formulas / Key Facts

| Concept | Formula | |---------|---------| | Profit | Profit = SP − CP | | Loss | Loss = CP − SP | | Profit % | Profit% = (Profit / CP) × 100 | | Loss % | Loss% = (Loss / CP) × 100 | | SP when Profit% given | SP = CP × (100 + Profit%) / 100 | | SP when Loss% given | SP = CP × (100 − Loss%) / 100 | | CP when SP and Profit% given | CP = SP × 100 / (100 + Profit%) | | CP when SP and Loss% given | CP = SP × 100 / (100 − Loss%) | | Discount | Discount = MP − SP | | Discount % | Discount% = (Discount / MP) × 100 | | SP after Discount | SP = MP × (100 − Discount%) / 100 |

**Key Facts to Remember:** 1. Profit and Loss percentages are always calculated on CP, never on SP. 2. Discount percentage is always calculated on MP, never on CP or SP. 3. If there is no discount, then MP = SP. 4. Two successive discounts of a% and b% are equivalent to a single discount of: a + b − (a × b)/100 percent.