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Basic Profit & Loss %

Introduction

In business and aptitude tests, questions on Profit and Loss are very common. They are based on the comparison between Cost Price (CP) and Selling Price (SP).

If SP > CP, there is a Profit. If SP < CP, there is a Loss.

To express this profit or loss clearly, we use percentage form.

Pattern: Basic Profit & Loss %

Pattern

The key idea is to calculate profit or loss % using CP as the base.

Profit = SP - CP
Loss = CP - SP
Profit % = (Profit ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100

Step-by-Step Example

Question

A shopkeeper buys an article for ₹200 and sells it for ₹250. Find the profit and profit %.

Options:

  • A. Profit ₹40, Profit % 20%
  • B. Profit ₹45, Profit % 22.5%
  • C. Profit ₹50, Profit % 25%
  • D. Profit ₹60, Profit % 30%

Solution

  1. Step 1: Identify CP and SP.

    CP = ₹200, SP = ₹250.

  2. Step 2: Calculate the profit amount.

    Profit = SP - CP = 250 - 200 = ₹50.

  3. Step 3: Calculate the profit percentage.

    Profit % = (50 ÷ 200) × 100 = 25%.

  4. Final Answer:

    Profit = ₹50 and Profit % = 25% → Option C

  5. Quick Check:

    25% of 200 = 50 ✅

Quick Variations

If SP = CP → No Profit, No Loss.

If SP = 120 and CP = 100 → Profit = 20, Profit % = 20%.

If SP = 80 and CP = 100 → Loss = 20, Loss % = 20%.

Trick to Always Use

  • Profit % or Loss % is always calculated on CP.
  • If % is given, use reverse formula → SP = CP × (1 ± %/100).
  • Memorize: “Base is always CP” ✅

Summary

Summary

  • Always compare SP and CP to decide profit or loss.
  • Use CP as the base for calculating percentages.
  • Profit = SP - CP and Loss = CP - SP.
  • Profit % or Loss % = (Difference ÷ CP) × 100.

Example to remember:
If CP = ₹200 and SP = ₹250 → Profit % = 25%

Practice

(1/5)
1. A pen is bought for ₹40 and sold for ₹50. Find the profit %.
easy
A. 20%
B. 22%
C. 25%
D. 15%

Solution

  1. Step 1: Identify CP and SP.

    CP = 40, SP = 50.

  2. Step 2: Calculate profit.

    Profit = 50 - 40 = 10.

  3. Step 3: Compute profit percentage.

    Profit % = (10 ÷ 40) × 100 = 25%.

  4. Final Answer:

    Profit % = 25% → Option C

  5. Quick Check:

    25% of 40 = 10 ✅
Hint: Profit % = (SP - CP)/CP × 100.
Common Mistakes: Taking SP as base instead of CP.
2. A book was purchased for ₹120 and sold for ₹96. Find the loss %.
easy
A. 15%
B. 18%
C. 20%
D. 25%

Solution

  1. Step 1: Identify CP and SP.

    CP = 120, SP = 96.

  2. Step 2: Calculate loss.

    Loss = 120 - 96 = 24.

  3. Step 3: Compute loss percentage.

    Loss % = (24 ÷ 120) × 100 = 20%.

  4. Final Answer:

    Loss % = 20% → Option C

  5. Quick Check:

    20% of 120 = 24 ✅
Hint: Loss % = (CP - SP)/CP × 100.
Common Mistakes: Using SP instead of CP for denominator.
3. If an article is bought for ₹500 and sold for ₹600, what is the profit %?
easy
A. 15%
B. 18%
C. 20%
D. 25%

Solution

  1. Step 1: Identify CP and SP.

    CP = 500, SP = 600.

  2. Step 2: Calculate profit.

    Profit = 600 - 500 = 100.

  3. Step 3: Compute profit percentage.

    Profit % = (100 ÷ 500) × 100 = 20%.

  4. Final Answer:

    Profit % = 20% → Option C

  5. Quick Check:

    20% of 500 = 100 ✅
Hint: Profit % = Profit ÷ CP × 100.
Common Mistakes: Subtracting wrongly: 500 - 600.
4. A toy costs ₹150. It is sold at a profit of 15%. Find the selling price.
medium
A. ₹170.5
B. ₹172.5
C. ₹175.5
D. ₹180.5

Solution

  1. Step 1: Identify CP and profit %.

    CP = 150, Profit % = 15.

  2. Step 2: Calculate profit amount.

    Profit = (15 ÷ 100) × 150 = 22.5.

  3. Step 3: Calculate selling price.

    SP = CP + Profit = 150 + 22.5 = 172.5.

  4. Final Answer:

    Selling Price = ₹172.5 → Option B

  5. Quick Check:

    150 × 1.15 = 172.5 ✅
Hint: SP = CP × (1 + Profit % ÷ 100).
Common Mistakes: Forgetting to add profit back to CP.
5. A laptop was bought for ₹20,000 and sold at a loss of 10%. Find the selling price.
medium
A. ₹17,500
B. ₹18,000
C. ₹18,500
D. ₹19,000

Solution

  1. Step 1: Identify CP and loss %.

    CP = 20,000, Loss % = 10.

  2. Step 2: Calculate loss amount.

    Loss = (10 ÷ 100) × 20,000 = 2,000.

  3. Step 3: Calculate selling price.

    SP = CP - Loss = 20,000 - 2,000 = 18,000.

  4. Final Answer:

    Selling Price = ₹18,000 → Option B

  5. Quick Check:

    10% of 20,000 = 2,000; subtract = 18,000 ✅
Hint: SP = CP × (1 - Loss % ÷ 100).
Common Mistakes: Subtracting loss % from SP instead of CP.

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