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Basic Profit & Loss %

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Introduction

Business और aptitude exams में Profit and Loss पर questions बहुत common होते हैं। ये हमेशा Cost Price (CP) और Selling Price (SP) की तुलना पर आधारित रहते हैं।

अगर SP > CP → Profit होता है।
अगर SP < CP → Loss होता है।

Profit या Loss को clearly समझाने के लिए हम उसे percentage में बदलते हैं।

Pattern: Basic Profit & Loss %

Pattern: Basic Profit & Loss %

हमेशा CP को base मानकर profit या loss % calculate किया जाता है।

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

Step-by-Step Example

Question

एक shopkeeper ने ₹200 में एक वस्तु खरीदी और उसे ₹250 में बेचा। Profit और profit % निकालें।

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: CP और SP पहचानें

    CP = ₹200, SP = ₹250.

  2. Step 2: Profit निकालें

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

  3. Step 3: Profit % निकालें

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

  4. Final Answer:

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

  5. Quick Check:

    25% of 200 = 50 ✅

Quick Variations

SP = CP → No Profit, No Loss.

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

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

Trick to Always Use

  • Profit % या Loss % हमेशा CP पर निकाला जाता है।
  • अगर % दिया हो → Reverse formula: SP = CP × (1 ± %/100).
  • याद रखें: “Base is always CP” ✅

Summary

  • SP और CP compare करके profit या loss decide करें।
  • Percentage निकालते समय base = CP रखें।
  • Profit = SP - CP, Loss = CP - SP.
  • Profit % या Loss % = (Difference ÷ CP) × 100.

Example to remember:
CP = ₹200, 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.