Profit, Loss, Discount and Interest
Profit, Loss, Discount and Interest
Commercial arithmetic gives 1 to 2 questions in the Part-II maths block, and they are formula-driven rather than tricky. The whole topic rests on one habit: always work percentages on the correct base — cost price for profit, marked price for discount, principal for interest.
Profit and Loss: Everything Runs on Cost Price
Profit = SP − CP | Profit % = (Profit ÷ CP) × 100
Loss follows the same shape with CP − SP. The base is always cost price, never selling price. This is the most common error in the topic.
✗ Bought at 400, sold at 500, profit = 100/500 = 20% | ✓ Bought at 400, sold at 500, profit = 100/400 = 25%
SP = CP × (100 + Profit %) ÷ 100
A shopkeeper in Chhapra buys a school bag for Rs 400 and wants 25% profit. SP = 400 × 125 ÷ 100 = Rs 500.
Marked Price and Discount
Discount is always calculated on the marked price, not the cost price. Profit is then measured from cost price. Keeping the two bases separate solves most questions in this area.
SP = MP × (100 − Discount %) ÷ 100
For two discounts one after the other, use the same successive formula you learnt in percentage: successive discounts of 20% and 10% are not 30% but 20 + 10 − (20 × 10) ÷ 100 = 28%.
Simple Interest and Compound Interest
SI = (P × R × T) ÷ 100
Amount in CI = P × (1 + R÷100)ⁿ | CI = Amount − P
| Point | Simple Interest | Compound Interest |
|---|---|---|
| Base | Principal stays fixed | Principal grows each year |
| Yearly interest | Same every year | Increases every year |
| Year 1 interest | Equal to CI of year 1 | Equal to SI of year 1 |
| Growth pattern | Straight line | Curved, faster |
| Exam frequency | More common | Usually two-year cases |
For two years the gap between the two has a clean shortcut, and it is asked directly.
CI − SI (2 years) = P × (R ÷ 100)²
If P = Rs 5,000 and R = 10%, the two-year difference is 5000 × (0.1)² = Rs 50.
लाभ हमेशा क्रय मूल्य पर, छूट हमेशा अंकित मूल्य पर — आधार बदलना सबसे बड़ी गलती है।
TRE pointer: In teaching-exam papers this topic is usually set in a small retail or school-supply context rather than as bare numbers — uniform sets, notebooks, a fair-price shop. Two traps repeat: calculating profit percent on selling price, and adding two successive discounts. The two-year CI − SI shortcut is worth memorising because it turns a three-step question into one line, which matters when you have about a minute per question.
60-Second Recap
- Profit % and loss % are always on cost price; discount % is always on marked price.
- SP = CP × (100 + P%)/100 and SP = MP × (100 − D%)/100.
- Successive discounts use a + b + ab/100 with negative signs, so 20% and 10% give 28%.
- SI = PRT/100; CI amount = P(1 + R/100)ⁿ.
- First-year SI and CI are always equal.
- CI − SI for two years = P(R/100)².
Frequently Asked Questions
Is profit percentage calculated on cost price or selling price?
Always on cost price, unless the question explicitly says otherwise. Profit percent equals profit divided by cost price, times 100. Candidates lose this mark regularly by dividing by the selling price, and examiners deliberately include that wrong value among the five options.
What is the difference between marked price and cost price?
Cost price is what the seller paid. Marked price is the label price before any discount. Discount is deducted from the marked price to get the selling price, and profit or loss is then measured against the cost price. Mixing the two bases is the main source of error.
Are two successive discounts of 20% and 10% the same as 30%?
No. They come to 28%, because the second discount applies to the already reduced price. Use a + b + ab/100 with both values negative, which gives −20 − 10 + 2 = −28. The single equivalent discount is therefore 28 percent.
How much simple interest and compound interest do I need for TRE?
Only the basics: the SI formula, the CI amount formula for two or three years, the fact that first-year interest is identical in both, and the two-year difference shortcut. Questions stay at class 7-8 level, so half-yearly compounding and complex instalment sums are not the priority.