Profit & Loss – PGECET Study Notes
Subject: Quantitative Aptitude
Exam: PGECET
Topic: Profit & Loss
These notes contain a concise explanation, key formulas, a worked example, and a quick revision summary to help you master Profit & Loss concepts for the PGECET exam.
1. Simple Explanation
- Profit = Selling Price (SP) – Cost Price (CP).
- Loss = Cost Price (CP) – Selling Price (SP).
- Profit or loss is expressed as a percentage of the CP (or sometimes of the SP).
The key idea: Profit is earned when SP > CP, and loss occurs when SP < CP.
2. Key Points & Formulas
| Concept | Formula | Notes |
|---|---|---|
| Profit / Loss (absolute) | ( \text{Profit} = SP - CP ) ( \text{Loss} = CP - SP ) |
Positive value indicates profit, negative indicates loss. |
| Profit % (on CP) | ( % \text{Profit} = \dfrac{SP-CP}{CP} \times 100 ) | Standard definition in most aptitude problems. |
| Loss % (on CP) | ( % \text{Loss} = \dfrac{CP-SP}{CP} \times 100 ) | |
| Profit % (on SP) | ( % \text{Profit on SP} = \dfrac{SP-CP}{SP} \times 100 ) | Occasionally used; remember denominator is SP. |
| Loss % (on SP) | ( % \text{Loss on SP} = \dfrac{CP-SP}{SP} \times 100 ) | |
| Markup % | ( % \text{Markup} = \dfrac{SP-CP}{CP} \times 100 ) | Same as profit % on CP; used in retail. |
| Markdown (Discount) % | ( % \text{Discount} = \dfrac{CP-SP}{CP} \times 100 ) | When selling below cost. |
| Ratio of Profit to Loss | ( \dfrac{\text{Profit}}{\text{Loss}} = \dfrac{SP-CP}{CP-SP} ) | Useful for two‑item problems. |
| Profit/Loss on Multiple Items | ( \text{Total Profit} = \sum (SP_i - CP_i) ) | Compute each item and sum. |
| Average Profit % | ( % \text{Average Profit} = \dfrac{\text{Total Profit}}{\text{Total CP}} \times 100 ) | |
| Break‑Even Point (in units) | ( BEU = \dfrac{\text{Fixed Cost}}{\text{Selling Price per unit} - \text{Variable Cost per unit}} ) | When total revenue = total cost. |
| Break‑Even Point (in rupees) | ( BE = BEU \times \text{Selling Price per unit} ) |
3. Worked Example
Problem (PGECET style)
A shopkeeper sells 3 items:
- Item A: 10% profit, sells 50 units.
- Item B: 20% loss, sells 80 units.
- Item C: 15% profit, sells 30 units.
The cost price of each unit of the items are ₹120, ₹200, and ₹150 respectively.
Find the overall profit percentage on the total cost.
Solution
- Compute CP and SP for each item
| Item | CP per unit | Units | Total CP | Profit% | SP per unit | Total SP |
|---|---|---|---|---|---|---|
| A | ₹120 | 50 | ₹120 × 50 = ₹6,000 | +10% | ₹120 × 1.10 = ₹132 | ₹132 × 50 = ₹6,600 |
| B | ₹200 | 80 | ₹200 × 80 = ₹16,000 | –20% | ₹200 × 0.80 = ₹160 | ₹160 × 80 = ₹12,800 |
| C | ₹150 |