Profit & Loss – XAT Quick‑Study Notes
XAT – Quantitative Ability – Profit & Loss
Exam‑type: Numerical & analytical reasoning
Time to master: 20‑25 minutes
1. Simple Explanation
| Term | Meaning | Example |
|---|---|---|
| Profit | Gain obtained when selling price (SP) > cost price (CP) | SP = ₹120, CP = ₹80 → Profit = ₹40 |
| Loss | Deficit when SP < CP | SP = ₹70, CP = ₹100 → Loss = ₹30 |
| Profit % | (Profit ÷ CP) × 100 | Profit ₹40 on CP ₹80 → 50 % profit |
| Loss % | (Loss ÷ CP) × 100 | Loss ₹30 on CP ₹100 → 30 % loss |
Key formulae
- SP = CP + Profit
- SP = CP – Loss
- Profit % = (Profit ÷ CP) × 100
- Loss % = (Loss ÷ CP) × 100
- If SP is known, CP = SP ÷ (1 ± %/100)
- For profit:
CP = SP / (1 + profit %/100) - For loss:
CP = SP / (1 – loss %/100)
- For profit:
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Use percentages as decimals (e.g., 20 % = 0.20). | Avoids mistakes in division. |
| 2 | Profit % uses CP as base. | Profit 20 % of ₹200 = ₹40; CP must be known. |
| 3 | Loss % also uses CP as base. | Loss 25 % of ₹200 = ₹50. |
| 4 | SP is the end value. | All calculations revolve around CP and SP. |
| 5 | When both CP & SP are unknown, use algebra. | Set variables and solve linear equations. |
| 6 | Unit‑sale problems (e.g., “sold x units at y% profit”). | Treat each unit the same for quick calculation. |
| 7 | Multi‑stage profit/loss (e.g., sold at 10 % profit, later bought at 20 % loss). | Use chain multiplication or find effective CP. |
| 8 | Marking scheme: 1‑2 marks each question; speed matters. | Practice mental arithmetic for % calcs. |
| 9 | Check for “percentage of total” vs “percentage of CP”. | Misreading leads to wrong answers. |
| 10 | Keep a “profit‑loss cheat sheet” with quick formulas. | For last‑minute revision. |
3. Worked Example
Question (XAT‑style):
A shopkeeper bought a set of pencils for ₹500. He sold them at a 20 % profit. Later, he bought the same pencils again at a 10 % loss on the selling price. What is the total cost price of the pencils after the second purchase?
Solution
-
First purchase
- CP₁ = ₹500
- Profit % = 20 % → Profit = 20 % of ₹500 = ₹100
- SP₁ = ₹500 + ₹100 = ₹600
-
Second purchase (cost on SP₁ but at 10 % loss)
- Loss % = 10 % → Loss = 10 % of SP₁ = 0.10 × ₹600 = ₹60
- CP₂ = SP₁ – Loss = ₹600 – ₹60 = ₹540
-
Total CP (after both purchases)
- CP_total = CP₁ + CP₂ = ₹500 + ₹540 = ₹1,040
Answer: ₹1,040
Quick Mental Math Trick
- 20 % of ₹500 = 10 % × 5 = ₹50 × 2 = ₹100
- 10 % of ₹600 = ₹60
- Add ₹500 + ₹540 → ₹1,040
4. Quick Revision Summary
- Profit = SP – CP → Profit % = (Profit ÷ CP) × 100
- Loss = CP – SP → Loss % = (Loss ÷ CP) × 100
- CP from SP
- Profit:
CP = SP ÷ (1 + profit %/100) - Loss:
CP = SP ÷ (1 – loss %/100)
- Profit:
- Percentage on a known amount:
(percent ÷ 100) × amount - Algebraic setup:
- Let CP = x, Profit % = p.
- SP = x(1 + p/100).
- If SP is known, solve for x.
- Chain problems: treat each stage separately, then combine.
- Common pitfalls:
- Confusing “profit on CP” vs “profit on SP”.
- Using
+when loss should be-. - Forgetting to divide by 100 when converting to decimal.
Final Tip
For XAT, you’ll often see two‑step problems (buy → sell → buy again).
Break them into stages, write the CP and SP for each, then add up.
Keep a one‑page cheat sheet with the formulas above and practice 5–10 problems a day. Happy studying!