📚 Profit & Loss – Quantitative Aptitude (Himachal Pradesh Forest Guard)
Objective: Master the fundamentals of profit & loss, solve typical exam questions, and review quickly before the exam.
1. Simple Explanation
| Term | Meaning | Formula |
|---|---|---|
| Cost Price (CP) | Amount paid to buy an item or a batch of items. | – |
| Selling Price (SP) | Amount at which the item(s) are sold. | – |
| Profit | When SP > CP. | Profit = SP – CP |
| Loss | When SP < CP. | Loss = CP – SP |
| Profit % | Percentage of profit over cost price. | (\displaystyle \text{Profit%} = \frac{\text{Profit}}{\text{CP}}\times100) |
| Loss % | Percentage of loss over cost price. | (\displaystyle \text{Loss%} = \frac{\text{Loss}}{\text{CP}}\times100) |
Key Insight:
- Profit and Loss are just differences between selling and cost prices.
- The percentage is always taken with respect to the Cost Price (not selling price).
2. Key Points & Formulas
| Scenario | Formula | Example |
|---|---|---|
| Single item | (\displaystyle \text{Profit%} = \frac{SP-CP}{CP}\times100) | CP = ₹80, SP = ₹100 → Profit% = 25% |
| Multiple items (same CP) | (\displaystyle \text{Profit%} = \frac{(SP_1 + SP_2 + …) - (CP_1 + CP_2 + …)}{(CP_1 + CP_2 + …)}\times100) | 5 items, each CP ₹20, SP ₹25 → Profit% = ( \frac{125-100}{100}\times100 = 25% ) |
| Different CPs | Same as above, sum each CP and SP. | 2 items: CP₁ ₹30, CP₂ ₹70; SP₁ ₹40, SP₂ ₹90 → Profit% = ( \frac{130-100}{100}\times100 = 30% ) |
| Buying from two sources | (\displaystyle \text{Profit%} = \frac{(SP_1+SP_2)- (CP_1+CP_2)}{(CP_1+CP_2)}\times100) | 10 pens at ₹5 each from A, 5 pens at ₹6 each from B; sold all 15 at ₹7 each → Profit% = ... |
| Profit & Loss combined | If two groups yield different profit/loss, combine totals. | Group 1: profit 10%; Group 2: loss 5% → overall? |
| Rate of profit/loss | (\displaystyle \text{Rate} = \frac{\text{Profit or Loss}}{\text{CP}}\times100) | Same as above. |
| Reverse calculation | If SP or CP known & profit/loss % known → use (SP = CP(1 \pm \text{Rate}/100)) | CP ₹200, profit 25% → SP = 200×1.25 = ₹250 |
| Break‑even | SP = CP → 0% profit/loss |
Quick Formula Cheat‑Sheet
| What you need | Formula (simplified) |
|---|---|
| Profit % | ((SP-CP)/CP \times 100) |
| Loss % | ((CP-SP)/CP \times 100) |
| SP from CP & rate | (SP = CP(1 + \text{rate}/100)) |
| CP from SP & rate | (CP = SP/(1 + \text{rate}/100)) |
| Profit / Loss amount | (= CP \times \text{rate}/100) |
3. Worked Example
Problem:
A shopkeeper buys 10 shirts at ₹120 each and 5 trousers at ₹200 each. He sells all the shirts at ₹150 each and all the trousers at ₹250 each.
Find the overall profit percentage.
Step‑by‑Step Solution
-
Compute total Cost Price (CP)
[ CP = (10 \times 120) + (5 \times 200) = 1200 + 1000 = ₹2200 ] -
Compute total Selling Price (SP)
[ SP = (10 \times 150) + (5 \times 250) = 1500 + 1250 = ₹2750 ] -
Profit Amount
[ \text{Profit} = SP - CP = 2750 - 2200 = ₹550 ] -
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