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) % |
**Example 4: Successive Discounts** *A shirt has a marked price of ₹800. Two successive discounts of 10% and 20% are offered. Find the final selling price.*
After first discount (10%): 800 × 0.90 = ₹720 After second discount (20%): 720 × 0.80 = **₹576**
1. **Calculating profit/loss% on SP instead of CP** Wrong: Profit% = Profit/SP × 100. Correct: Always use CP as the base for profit% or loss%.
2. **Adding successive discounts directly** Wrong: 10% + 20% = 30% discount. Correct: Apply discounts sequentially or use the formula a + b − ab/100.
3. **Confusing MP with CP** Wrong: Assuming marked price equals cost price. Correct: MP is the labelled price; CP is what the seller paid. They are different unless stated otherwise.
4. **Ignoring the base in percentage increase/decrease** Wrong: "A is 25% more than B" treated same as "B is 25% less than A." Correct: If A = 125, B = 100, then A is 25% more than B, but B is 20% less than A.
5. **Using wrong multiplier for decrease** Wrong: 30% decrease = multiply by 1.30. Correct: 30% decrease = multiply by 0.70.
Quick Reference
Profit% and Loss% are always on **Cost Price**.
Discount% is always on **Marked Price**.
x% increase → multiply by (1 + x/100); x% decrease → multiply by (1 − x/100).
Two successive discounts of a% and b% = (a + b − ab/100)%.
To reverse a percentage: if SP = CP × 1.20, then CP = SP / 1.20.
A shopkeeper bought a chair for Rs 800 and sold it for Rs 920. What is his profit percentage?
Q2 · Percentage and Profit-Loss · MEDIUM
A shirt marked at Rs 1500 is sold at a discount of 20%. If the shopkeeper still makes a profit of 25%, what was the cost price of the shirt?
Q3 · Percentage and Profit-Loss · MEDIUM
In a school, 60% of the students are boys. If 15% of the boys and 10% of the girls passed the scholarship exam, what percentage of the total students passed the exam?
Q4 · Percentage and Profit-Loss · HARD
A trader marks his goods 40% above the cost price and allows a discount of 20%. He also uses a faulty weight of 900 grams instead of 1 kilogram. What is his overall profit percentage?
Q5 · Percentage and Profit-Loss · MEDIUM
A shopkeeper marks his goods 30% above the cost price but allows a discount of 15%. What is his net profit percentage?