Percentage and Profit-Loss

Overview

Percentage and Profit-Loss form the backbone of commercial arithmetic in MP TET Mathematics. These concepts appear directly in the exam and also serve as building blocks for related topics like Simple Interest, Compound Interest, Ratio-Proportion, and Data Interpretation. For a primary or upper-primary teacher, mastery of these concepts is essential—not just for the exam but for making everyday mathematics meaningful to students.

Expect 3–5 questions from this cluster in MP TET Varg-1, Varg-2, and Varg-3 papers. Questions typically involve straightforward percentage calculations, finding profit or loss percent, successive discounts, and word problems set in real-life contexts like shopping, farming, or local markets. The key to scoring well is conceptual clarity and quick mental calculation—avoid lengthy methods.

Key Concepts

• **Percentage means "per hundred"**: x% = x/100. Any fraction or decimal can be converted to percentage by multiplying by 100.

• **Base value matters**: When we say "A is 20% more than B," the base is B. When we say "A is 20% less than B," again the base is B. Identifying the correct base prevents most errors.

• **Cost Price (CP)** is the price at which an article is purchased. **Selling Price (SP)** is the price at which it is sold.

• **Profit = SP − CP** (when SP > CP). **Loss = CP − SP** (when CP > SP). Profit% and Loss% are always calculated on CP.

• **Marked Price (MP)** is the listed/labelled price. **Discount** is the reduction given on MP. So, SP = MP − Discount.

• **Successive discounts** are not additive. Two discounts of 10% and 20% do not equal 30%. They must be applied one after another.

• **Multiplying factors** speed up calculations: a 20% increase corresponds to multiplying by 1.20; a 20% decrease corresponds to multiplying by 0.80.

• **Percentage change formula**: Change% = (Change / Original) × 100. This single formula covers increase, decrease, profit, and loss calculations.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Percentage of a number | x% of N = (x/100) × N | | Fraction to Percentage | (a/b) × 100 | | Profit | Profit = SP − CP | | Loss | Loss = CP − SP | | Profit % | (Profit / CP) × 100 | | Loss % | (Loss / CP) × 100 | | SP when Profit% given | SP = CP × (1 + P%/100) | | SP when Loss% given | SP = CP × (1 − L%/100) | | Discount | Discount = MP − SP | | Discount % | (Discount / MP) × 100 | | SP after discount | SP = MP × (1 − D%/100) | | Two successive discounts a% and b% | Equivalent single discount = a + b − (ab/100) % | | Two successive increases a% and b% | Net increase = a + b + (ab/100) % |