📚 Profit & Loss – Uttarakhand PSC – Quantitative Aptitude
Why you need this?
Profit & Loss problems form the backbone of many quantitative aptitude questions in the Uttarakhand PSC exam. Mastering the basic formulas and the “shortcut” methods will save you time and reduce errors.
1️⃣ Simple Explanation
| Term | Meaning | Formula |
|---|---|---|
| Cost Price (CP) | The amount paid to acquire an item. | (CP) |
| Selling Price (SP) | The amount received when selling the item. | (SP) |
| Profit | (SP - CP) (positive when (SP>CP)). | (Profit = SP - CP) |
| Loss | (CP - SP) (positive when (CP>SP)). | (Loss = CP - SP) |
| Profit % | Ratio of profit to cost price, expressed as a percentage. | (\displaystyle Profit% = \frac{SP-CP}{CP}\times 100) |
| Loss % | Ratio of loss to cost price, expressed as a percentage. | (\displaystyle Loss% = \frac{CP-SP}{CP}\times 100) |
Key Insight – All problems boil down to manipulating these two simple formulas.
2️⃣ Key Points & Tricks
| # | Point | Quick Tip |
|---|---|---|
| 1 | Use “price + percentage” to find SP. | If CP = 200 and profit% = 25%, SP = 200 × (1 + 0.25) = 250. |
| 2 | Use “price – percentage” to find SP. | If CP = 200 and loss% = 10%, SP = 200 × (1 – 0.10) = 180. |
| 3 | Profit% = (SP-CP)/CP × 100 – always divide by CP. | Do the division first, then multiply by 100. |
| 4 | Loss% = (CP-SP)/CP × 100 – same rule. | |
| 5 | If you know CP and % gain/loss, you can compute SP directly. | Avoid computing profit/loss first. |
| 6 | If you know SP and % gain/loss, find CP. | CP = SP ÷ (1 + profit%) or CP = SP ÷ (1 – loss%). |
| 7 | Percentage change between two values | (\displaystyle \frac{New - Old}{Old}\times 100) |
| 8 | Unit price method – handy for mix problems. | Divide total cost or revenue by quantity to get per‑unit price. |
| 9 | Check for “percentage of profit” vs “percentage increase” | The formula is identical but the context matters. |
| 10 | Practice unit‑price problems – they appear frequently in PSC tests. |
3️⃣ Worked Example
Problem
A shopkeeper buys 10 identical items for ₹300 each. He wants a 20 % profit on the total sale.
What should be the selling price per item?
Step‑by‑Step
| Step | Calculation | Result |
|---|---|---|
| 1 | Find total cost price (TCP) | (10 \times 300 = ₹3000) |
| 2 | Compute profit amount | (20% \text{ of } 3000 = 0.20 \times 3000 = ₹600) |
| 3 | Find total selling price (TSP) | (TCP + Profit = 3000 + 600 = ₹3600) |
| 4 | Divide by number of items for unit price | (3600 ÷ 10 = ₹360) |
Answer: ₹360 per item.
Quick Formula Check
(SP = CP \times (1 + \frac{profit%}{100}) = 300 \times (1 + 0.20) = 360).
4️⃣ Quick Revision Summary
- Profit = SP – CP
- Loss = CP – SP
- Profit % = (\frac{SP-CP}{CP}\times 100)
- Loss % = (\frac{CP-SP}{CP}\times 100)
- SP from CP & %: (SP = CP \times (1 \pm \frac{percentage}{100}))
- CP from SP & %: (CP = \frac{SP}{1 \pm \frac{percentage}{100}})
Remember:
- “+” for profit, “‑” for loss.
- Always divide by CP to get the percentage.
- Use the unit‑price method for mix‑item problems.
📌 Practice Tip
Create a quick table with CP, SP, Profit/Loss, % for a set of numbers and solve in both directions. Repeating this will cement the formulas and make your calculation speed razor‑sharp for the PSC exam.