Profit and Loss (P&L) is a crucial topic in competitive exams and everyday business. Whether you're preparing for bank exams, SSC, or just want to sharpen your math skills, mastering P&L can save time and boost accuracy. Let's break it down with easy formulas, Vedic math tricks, and real-life examples.
Basic Terms You Must Know
- Cost Price (CP): Price at which an item is purchased.
- Selling Price (SP): Price at which an item is sold.
- Profit (P): When SP > CP → Profit = SP – CP
- Loss (L): When CP > SP → Loss = CP – SP
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
Must-Know Formulas & Shortcuts
1. Finding SP when Profit/Loss % is Given
If Profit% (P%) is given:
\[ SP = CP \times \left(1 + \frac{P\%}{100}\right) \]
If Loss% (L%) is given:
\[ SP = CP \times \left(1 - \frac{L\%}{100}\right) \]
Example: If CP = ₹500, Profit = 20%, then SP = ?
SP = 500 × (1 + 20/100) = 500 × 1.2 = ₹600
2. Finding CP when SP and Profit/Loss % are Given
If Profit% (P%) is given:
\[ CP = \frac{SP \times 100}{100 + P\%} \]
If Loss% (L%) is given:
\[ CP = \frac{SP \times 100}{100 - L\%} \]
Example: If SP = ₹720, Loss = 10%, then CP = ?
CP = (720 × 100)/(100 - 10) = 72000/90 = ₹800
3. Quick Percentage Profit/Loss Calculation
\[ Profit\% = \left(\frac{SP - CP}{CP}\right) \times 100 \]
\[ Loss\% = \left(\frac{CP - SP}{CP}\right) \times 100 \]
Example: CP = ₹200, SP = ₹250 → Profit% = ?
\[ Profit\% = \left(\frac{250 - 200}{200}\right) \times 100 = 25\% \]
Vedic Math Tricks for Faster Calculations
1. Base Method for Profit/Loss % (When SP is Close to CP)
If SP is slightly higher/lower than CP:
For Profit:
\[ Profit\% ≈ \left(\frac{Difference}{CP}\right) \times 100 \]
For Loss:
\[ Loss\% ≈ \left(\frac{Difference}{CP}\right) \times 100 \]
Example: CP = ₹120, SP = ₹132 → Profit%?
Difference = ₹12
\[ Profit\% ≈ \left(\frac{12}{120}\right) \times 100 = 10\% \]
2. Successive Profit/Loss (Multiple Transactions)
If an item is sold at two successive profits (P₁% and P₂%), the net profit% is:
\[ Net Profit\% = P₁ + P₂ + \left(\frac{P₁ \times P₂}{100}\right) \]
Example: A shopkeeper sells an item at 10% profit and then again at 20% profit. Net profit?
\[ Net Profit\% = 10 + 20 + \left(\frac{10 \times 20}{100}\right) = 32\% \]
For Successive Profit & Loss, use:
\[ Net\% = P - L - \left(\frac{P \times L}{100}\right) \]
Example: First 20% profit, then 10% loss → Net effect?
\[ Net\% = 20 - 10 - \left(\frac{20 \times 10}{100}\right) = 8\% \text{ Profit} \]
Real-Life Examples & Common Exam Questions
1. Dishonest Shopkeeper (False Weight)
If a shopkeeper sells 900g instead of 1kg at CP, what's his profit%?
Trick:
\[ Profit\% = \left(\frac{True Weight - False Weight}{False Weight}\right) \times 100 \]
\[ Profit\% = \left(\frac{1000 - 900}{900}\right) \times 100 ≈ 11.11\% \]
2. Discount & Marked Price
- Marked Price (MP): Printed price before discount.
- Selling Price after Discount (D%):
\[ SP = MP \times \left(1 - \frac{D\%}{100}\right) \]
Example: MP = ₹1000, Discount = 25% → SP?
SP = 1000 × 0.75 = ₹750
Final Quick Tips
- ✔ Memorize key formulas for quick recall.
- ✔ Use approximation in percentage calculations to save time.
- ✔ Practice successive transactions (profit + loss scenarios).
- ✔ For false weight problems, always compare true vs. given weight.
Master these tricks, and Profit & Loss problems will become a cakewalk! 🚀
Got any doubts? Drop them in the comments! 😊
📜 Quiz Instructions
- ✅ Enter your name before starting the quiz.
- ⏳ Each question has 60 seconds to answer.
- 🎯 Each question carries 10 marks.
- 📊 Track your live score updates instantly.
- 🏆 Your total score will be shown at the end.
- 💬 Share how this quiz helps your job preparation!
- 📢 Need a quiz on a specific topic? Comment below!
- 💡 Keep practicing until you achieve 100%!
