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Profit, Loss & Discount

Introduction

Many percentage questions use basic profit, loss, and discount concepts. These are common in aptitude tests and in daily life (shopping, trading).

The core idea is to compare Cost Price (CP) and Selling Price (SP), or to apply a discount on a marked price. Once you know the formulas, these are straightforward.

Pattern: Profit, Loss & Discount

Pattern

The key idea:

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)

Use these formulas directly by translating the sentence into math.

Step-by-Step Example

Question

A shopkeeper buys an item at a cost price (CP) of 200 and sells it for a selling price (SP) of 240. Find the profit %.

Solution

  1. Step 1: Write CP and SP.

    Sentence: CP = 200, SP = 240.

  2. Step 2: Find absolute profit.

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

  3. Step 3: Compute profit % (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.

    20% of 200 = 40 → CP + 40 = 240 ✅ (matches SP)

Question

An item has a marked price (MP) of 1000. The shop offers a 20% discount. Find the discounted price.

Solution

  1. Step 1: Write MP and discount %.

    Sentence: MP = 1000, discount = 20%.

  2. Step 2: Convert discount to decimal.

    Sentence: Discount fraction = 20/100 = 0.20.

  3. Step 3: Compute discounted price (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 = 20% of 1000 = 200 → 1000 - 200 = 800 ✅

Quick Variations

If only profit % given: CP = SP ÷ (1 + profit%/100). Example: SP = 240, profit = 20% → CP = 240 ÷ 1.2 = 200.

If only loss % given: SP = CP × (1 - loss%/100).

Successive discounts: Two discounts of a% and b% on MP result in final factor = (1 - a/100) × (1 - b/100).

Trick to Always Use

  • Step 1: Identify CP, SP, or MP from the sentence.
  • Step 2: Use Profit = SP - CP and Profit% = (Profit ÷ CP) × 100.
  • Step 3: For discount, multiply MP by (1 - discount%/100).
  • Step 4: Use shortcuts: 10% = 1/10, 25% = 1/4, 20% = 1/5 to speed calculations.

Summary

Summary

The Profit, Loss & Discount pattern uses simple percentage formulas:

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

Translate the sentence → write the formula → compute → verify with a quick check.

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.

Mock Test

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