How to Solve Profit and Loss Problems

How to Solve Profit and Loss Problems

(For SSC, Bank, Railway Exams – Ace Your Exam with Confidence!)

Introduction

"Master profit and loss, and you unlock 5–10 marks in every SSC, Bank, or Railway exam—enough to push you from ‘just passing’ to ‘top 10%’! (On camera: Hold up a past paper with a circled profit/loss question.) "These questions look simple, but examiners hide traps in the wording. Today, you’ll learn the exact steps to solve them fast and error-free—no guessing, no panic."

What You Need To Know First

Before diving in, ensure you understand:
1. Percentage Basics – How to calculate % increase/decrease (e.g., 20% of 50 = 10).
2. Cost Price (CP) vs. Selling Price (SP) – CP = what you pay; SP = what you sell for.
3. Basic Arithmetic – Addition, subtraction, multiplication, and division (no calculators in exams!).

(On camera: Quick check-in) "Raise your hand if you can find 15% of 200 in 5 seconds. (Pause) Good! If not, pause here and practice percentages first—this guide won’t work without them."

Key Vocabulary

(On camera: Point to each term) "Memorize these like your exam depends on it—because it does! No shortcuts here."

Formulas To Know

(Write these on a board or slide. Circle the ones to memorize.)

1. Profit = SP – CP
2. Variables: SP = Selling Price, CP = Cost Price.

3. Memorise This. – It’s the foundation.

4. Loss = CP – SP

5. Variables: Same as above.

6. Memorise This. – Opposite of profit.

7. Profit % = (Profit / CP) × 100

8. Variables: Profit = SP – CP.

9. Memorise This. – Exams never give this formula.

10. Loss % = (Loss / CP) × 100

11. Variables: Loss = CP – SP.

12. Memorise This. – Same as profit %, but for loss.

13. SP = CP × (1 + Profit%/100)

14. Variables: Profit% = profit percentage.

15. Memorise This. – Use when CP and profit% are given.

16. SP = CP × (1 – Loss%/100)

17. Variables: Loss% = loss percentage.

18. Memorise This. – Use when CP and loss% are given.

19. CP = SP / (1 + Profit%/100)

20. Variables: Use when SP and profit% are given.

21. Memorise This. – Reverse of formula 5.

22. CP = SP / (1 – Loss%/100)

23. Variables: Use when SP and loss% are given.

24. Memorise This. – Reverse of formula 6.

25. Discount = MP – SP

26. Variables: MP = Marked Price.

27. Given on exam sheet (but still useful to know).

28. Discount % = (Discount / MP) × 100

    • Variables: Discount = MP – SP.
    • Memorise This. – Exams test this often.

(On camera: Hold up a formula sheet) "These 10 formulas cover 99% of exam questions. Write them down now—don’t skip this!

Step-by-Step Method

(On camera: Write steps on a whiteboard as you explain.)

Step 1: Read the question carefully. - Underline CP, SP, Profit, Loss, MP, Discount. - Circle percentages (e.g., 20% profit, 10% discount).

Step 2: Identify what’s given and what’s asked. - Example: "A shopkeeper buys a book for ₹200 and sells it at a 15% profit. Find SP." - Given: CP = ₹200, Profit% = 15%. - Asked: SP = ?

Step 3: Choose the right formula. - Use SP = CP × (1 + Profit%/100) for profit. - Use SP = CP × (1 – Loss%/100) for loss.

Step 4: Plug in the numbers. - For the example: SP = 200 × (1 + 15/100) = 200 × 1.15 = ₹230.

Step 5: Check units and answer the question. - Ensure the answer is in ₹, %, or units as asked. - Write: "The selling price is ₹230."

Step 6: Verify with common sense. - If CP = ₹200 and profit = 15%, SP must be > ₹200. - If your answer is ₹180, you made a mistake!

Worked Example Using Steps

Question: A trader buys a chair for ₹800 and sells it at a 25% profit. Find the selling price.

Step 1: Underline key info. - CP = ₹800, Profit% = 25%, Find SP.

Step 2: Given: CP, Profit%. Asked: SP.

Step 3: Use SP = CP × (1 + Profit%/100).

Step 4: SP = 800 × (1 + 25/100) = 800 × 1.25 = ₹1000.

Step 5: Answer: The selling price is ₹1000.

Step 6: Check: ₹1000 > ₹800 (profit), so it makes sense.

(On camera: Solve this live, showing each step.) "See how easy it is when you follow the steps? No guessing, no errors!"

Worked Examples

Example 1 – Basic

Question: A man buys a cycle for ₹1200 and sells it for ₹1500. Find his profit percentage.

Solution:
1. CP = ₹1200, SP = ₹1500.
2. Profit = SP – CP = 1500 – 1200 = ₹300.
3. Profit % = (Profit / CP) × 100 = (300 / 1200) × 100 = 25%.

Answer: 25% profit.

What we did and why: - We used Profit = SP – CP to find the profit amount. - Then, Profit % = (Profit / CP) × 100 to convert it to a percentage. - Key: Always divide by CP, not SP!

Example 2 – Medium

Question: A shopkeeper sells a fan for ₹1800 at a 10% loss. Find the cost price.

Solution:
1. SP = ₹1800, Loss% = 10%.
2. Use CP = SP / (1 – Loss%/100).
3. CP = 1800 / (1 – 10/100) = 1800 / 0.9 = ₹2000.

Answer: The cost price is ₹2000.

What we did and why: - We used the reverse formula because SP and loss% were given. - Key: For loss, subtract the % from 1 (1 – 10/100 = 0.9).

Example 3 – Exam-Style (Disguised Question)

Question: By selling 33 meters of cloth, a shopkeeper gains the cost price of 11 meters. Find his profit percentage.

Solution:
1. Let CP of 1 meter = ₹x. - CP of 33 meters = ₹33x. - SP of 33 meters = CP of 33 meters + Profit = 33x + 11x = ₹44x.
2. Profit = SP – CP = 44x – 33x = ₹11x.
3. Profit % = (Profit / CP) × 100 = (11x / 33x) × 100 = (1/3) × 100 ≈ 33.33%.

Answer: 33.33% profit.

What we did and why: - The question doesn’t give numbers, so we assumed CP = ₹x. - Key: Profit is given in terms of CP (11 meters), so we set up an equation. - Trap: Don’t assume CP = 1! Use variables.

Common Mistakes

(On camera: Hold up a wrong answer) "See this? ₹180 instead of ₹230. Why? Because they divided by SP, not CP. Don’t be that student!"

Exam Traps

(On camera: Show a tricky question) "Examiners love this trap: ‘A sells at 20% profit on SP.’ Run! It’s a trick. Profit is always on CP."

1-Minute Recap

(On camera: Speak naturally, like a pep talk.)

"Alright, listen up—this is your last-minute cheat sheet for profit and loss:

1. Underline CP, SP, Profit, Loss, MP, Discount in the question.
2. Pick the right formula—if you have CP and profit%, use SP = CP × (1 + Profit%/100).
3. For loss, subtract the % from 1: SP = CP × (1 – Loss%/100).
4. Reverse formulas if you have SP and %: CP = SP / (1 ± %/100).
5. Check units—₹ or %? Don’t mix them up!
6. Watch for traps—profit on SP? Discounts? Successive profits? Slow down and read twice.
7. Verify—if CP is ₹100 and profit is 20%, SP must be ₹120. If not, redo it!

Tonight’s homework: Solve 5 questions using these steps. No shortcuts! Tomorrow, you’ll solve them in under 30 seconds—guaranteed.

Now go ace that exam!