Profit & Loss – Study Notes
(LIC ADO – Quantitative Aptitude)
1. Simple Explanation
- Cost Price (CP) – the amount paid for an item or goods.
- Selling Price (SP) – the amount received when the item is sold.
- Profit –
SP > CP. - Loss –
SP < CP.
The profit or loss amount is simply SP – CP.
The profit or loss percentage tells how large that amount is relative to the cost price.
Key idea – All calculations in profit & loss are based on percentages of the cost price.
2. Key Points
| Concept | What it Means | How to Compute |
|---|---|---|
| Profit / Loss | Difference between SP and CP | Profit = SP – CP Loss = CP – SP |
| Profit/Loss % | Relative to CP | %Profit = (Profit ÷ CP) × 100 %Loss = (Loss ÷ CP) × 100 |
| Selling Price | CP plus profit (or minus loss) | SP = CP × (1 ± %Profit/100) |
| Cost Price | SP minus profit (or plus loss) | CP = SP ÷ (1 ± %Profit/100) |
| Discount | Reduction on marked‑up price | Discount % = (Discount ÷ Marked Price) × 100 |
| Markup | Increase on cost to get marked price | Markup % = (Marked Price – CP) ÷ CP × 100 |
| Multiple Items | Use weighted averages | Avg CP = Σ (CP_i × Qty_i) ÷ Σ Qty_i Avg SP = Σ (SP_i × Qty_i) ÷ Σ Qty_i |
Important – All percentages are applied to the cost price unless stated otherwise.
3. Formulas (Quick Reference)
| Quantity | Formula | Example |
|---|---|---|
| Profit % | [(SP – CP) ÷ CP] × 100 |
[(120 – 100) ÷ 100] × 100 = 20% |
| Loss % | [(CP – SP) ÷ CP] × 100 |
[(100 – 80) ÷ 100] × 100 = 20% |
| SP (given CP & %Profit) | CP × (1 + %Profit/100) |
100 × 1.20 = 120 |
| CP (given SP & %Loss) | SP ÷ (1 – %Loss/100) |
80 ÷ 0.80 = 100 |
| Discount % | [(Marked Price – SP) ÷ Marked Price] × 100 |
[(120 – 100) ÷ 120] × 100 = 16.67% |
| Markup % | [(Marked Price – CP) ÷ CP] × 100 |
[(120 – 100) ÷ 100] × 100 = 20% |
| Average CP (multiple items) | Σ (CP_i × Qty_i) ÷ Σ Qty_i |
– |
| Average SP | Σ (SP_i × Qty_i) ÷ Σ Qty_i |
– |
| Overall % Profit/Loss (multiple items) | [(Avg SP – Avg CP) ÷ Avg CP] × 100 |
– |
4. Worked Example
Problem
A shopkeeper buys 5 packets of biscuits at a 25 % discount on the marked price.
The marked price of one packet is ₹200.
He sells each packet at a 15 % profit on its cost price.
What is the selling price of one packet?
Step‑by‑step
| Step | What to Find | Calculation | Result |
|---|---|---|---|
| 1 | Marked Price (MP) of one packet | Given | ₹200 |
| 2 | Discount on MP | 25 % of 200 |
0.25 × 200 = ₹50 |
| 3 | Cost Price (CP) of one packet | MP – Discount |
200 – 50 = ₹150 |
| 4 | Profit on CP | 15 % of CP |
0.15 × 150 = ₹22.50 |
| 5 | Selling Price (SP) | CP + Profit |
150 + 22.50 = ₹172.50 |
Answer: The selling price of one packet is ₹172.50.
Quick mental‑math trick
- To add a 15 % profit to ₹150:
`15 % of 150 = 10 % (15) + 5 % (7.5)