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Profit, Loss & Discount

Introduction

कई percentage वाले questions में basic profit, loss, and discount concepts का use होता है। ये aptitude tests और daily life (shopping, trading) दोनों में common हैं।

Core idea है Cost Price (CP) और Selling Price (SP) की तुलना करना, या किसी marked price पर discount apply करना। Formulas पता हों तो ये questions काफी आसान होते हैं।

Pattern: Profit, Loss & Discount

Pattern

मुख्य बात:

Profit (absolute) = SP - CP
Profit % = ((SP - CP) ÷ CP) × 100
Loss % = ((CP - SP) ÷ CP) × 100
Discount on Marked Price (MP): Discounted Price = MP × (1 - discount%/100)

Sentence को math में convert करके directly इन formulas का use करें।

Step-by-Step Example

Question

एक shopkeeper किसी item को cost price (CP) of 200 पर खरीदता है और selling price (SP) of 240 पर बेचता है। profit % निकालें।

Solution

  1. Step 1: CP और SP लिखें।

    Sentence: CP = 200, SP = 240.

  2. Step 2: Absolute profit निकालें।

    Sentence: Profit = SP - CP.
    Math: Profit = 240 - 200 = 40.

  3. Step 3: Profit % निकालें (Sentence → Math)।

    Sentence: Profit % = (Profit ÷ CP) × 100.
    Math: Profit % = (40 ÷ 200) × 100 = 0.2 × 100 = 20%.

  4. Step 4: Final Answer.

    Profit % = 20%

  5. Step 5: Quick Check.

    200 का 20% = 40 → CP + 40 = 240 ✅ (SP match करता है)

Question

एक item का marked price (MP) of 1000 है। Shop में 20% discount दिया जा रहा है। discounted price निकालें।

Solution

  1. Step 1: MP और discount % लिखें।

    Sentence: MP = 1000, discount = 20%.

  2. Step 2: Discount को decimal में बदलें।

    Sentence: Discount fraction = 20/100 = 0.20.

  3. Step 3: Discounted price निकालें (Sentence → Math)।

    Sentence: Discounted price = MP × (1 - discount fraction).
    Math: Discounted price = 1000 × (1 - 0.20) = 1000 × 0.80 = 800.

  4. Step 4: Final Answer.

    Discounted price = 800

  5. Step 5: Quick Check.

    Discount amount = 1000 का 20% = 200 → 1000 - 200 = 800 ✅

Quick Variations

अगर सिर्फ profit % दिया है: CP = SP ÷ (1 + profit%/100). Example: SP = 240, profit = 20% → CP = 240 ÷ 1.2 = 200.

अगर सिर्फ loss % दिया है: SP = CP × (1 - loss%/100).

Successive discounts: दो discounts a% और b% हों तो final factor = (1 - a/100) × (1 - b/100) होगा।

Trick to Always Use

  • Step 1: Sentence से CP, SP, या MP पहचानें।
  • Step 2: Profit = SP - CP और Profit% = (Profit ÷ CP) × 100 का use करें।
  • Step 3: Discount के लिए MP × (1 - discount%/100) multiply करें।
  • Step 4: Shortcuts use करें: 10% = 1/10, 25% = 1/4, 20% = 1/5 calculation fast करने के लिए।

Summary

Summary

Profit, Loss & Discount pattern में simple percentage वाले formulas use होते हैं:

  • Profit % = ((SP - CP) ÷ CP) × 100
  • Loss % = ((CP - SP) ÷ CP) × 100
  • Discounted Price = MP × (1 - discount%/100)

Sentence → formula → calculation → quick check करके verify करें।

Practice

(1/5)
1. A shopkeeper bought an item at ₹200 and sold it for ₹240. Find the profit percentage.
easy
A. 15%
B. 20%
C. 25%
D. 30%

Solution

  1. Step 1: Identify CP and SP

    CP = 200, SP = 240.

  2. Step 2: Compute profit amount

    Profit = SP - CP = 240 - 200 = 40.

  3. Step 3: Calculate profit percentage

    Profit % = (Profit ÷ CP) × 100 → (40 ÷ 200) × 100 = .

  4. Final Answer:

    20% → Option B

  5. Quick Check:

    20% of 200 = 40 → 200 + 40 = 240 ✅
Hint: Profit % = (SP - CP)/CP × 100.
Common Mistakes: Dividing by SP instead of CP.
2. A shopkeeper bought an article for ₹500 and sold it for ₹450. Find the loss percentage.
easy
A. 8%
B. 9%
C. 10%
D. 12%

Solution

  1. Step 1: Identify CP and SP

    CP = 500, SP = 450.

  2. Step 2: Compute loss amount

    Loss = CP - SP = 500 - 450 = 50.

  3. Step 3: Calculate loss percentage

    Loss % = (Loss ÷ CP) × 100 → (50 ÷ 500) × 100 = .

  4. Final Answer:

    10% → Option C

  5. Quick Check:

    10% of 500 = 50 → 500 - 50 = 450 ✅
Hint: Loss % = (Loss ÷ CP) × 100.
Common Mistakes: Dividing by SP instead of CP.
3. An item has a marked price of ₹1,000. If a shopkeeper offers 20% discount, what is the selling price?
medium
A. ₹750
B. ₹780
C. ₹800
D. ₹820

Solution

  1. Step 1: Identify MP and discount

    MP = 1000, Discount = 20%.

  2. Step 2: Compute multiplier for selling price

    Selling price = MP × (1 - discount/100) = 1000 × (1 - 0.20) = 1000 × 0.80.

  3. Step 3: Calculate selling price

    1000 × 0.80 = .

  4. Final Answer:

    ₹800 → Option C

  5. Quick Check:

    20% of 1000 = 200 → 1000 - 200 = 800 ✅
Hint: Selling price = MP × (100 - discount)% ÷ 100.
Common Mistakes: Subtracting discount % instead of discount amount.
4. A trader sold a book at ₹540 and gained 8%. Find the cost price.
medium
A. ₹480
B. ₹500
C. ₹520
D. ₹540

Solution

  1. Step 1: Identify SP and profit%

    SP = 540, Profit% = 8%.

  2. Step 2: Use SP = CP × (1 + profit/100)

    540 = CP × 1.08 → CP = 540 ÷ 1.08.

  3. Step 3: Calculate CP

    CP = .

  4. Final Answer:

    ₹500 → Option B

  5. Quick Check:

    Profit = 8% of 500 = 40 → 500 + 40 = 540 ✅
Hint: CP = SP ÷ (1 + profit%).
Common Mistakes: Subtracting 8% directly instead of dividing.
5. A pen is bought at ₹120 and sold at ₹96. Find the loss percentage.
medium
A. 15%
B. 18%
C. 20%
D. 25%

Solution

  1. Step 1: Identify CP and SP

    CP = 120, SP = 96.

  2. Step 2: Compute loss amount

    Loss = CP - SP = 120 - 96 = 24.

  3. Step 3: Calculate loss percentage

    Loss % = (Loss ÷ CP) × 100 → (24 ÷ 120) × 100 = .

  4. Final Answer:

    20% → Option C

  5. Quick Check:

    20% of 120 = 24 → 120 - 24 = 96 ✅
Hint: Loss % = (CP - SP)/CP × 100.
Common Mistakes: Dividing by SP instead of CP.

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