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Overall Profit/Loss (Multiple Articles)

Introduction

Many real-world problems involve buying and selling multiple articles at different profits or losses. To evaluate the overall profit or loss, we must carefully compare the total Cost Price (CP) and total Selling Price (SP).

This pattern is important because it teaches how to aggregate results across multiple items, rather than treating them individually.

Pattern: Overall Profit/Loss (Multiple Articles)

Pattern

If CP > SP → Loss; If SP > CP → Profit.

Overall % = ((Total SP - Total CP) ÷ Total CP) × 100

Step-by-Step Example

Question

A shopkeeper buys 2 articles at ₹500 each. He sells one at 20% profit and the other at 10% loss. Find the overall profit or loss percent.

Options:

  • A. 5% profit
  • B. 2% profit
  • C. 5% loss
  • D. 10% profit

Solution

  1. Step 1: Calculate total cost price

    CP of first article = ₹500, CP of second = ₹500. Total CP = 500 + 500 = ₹1,000.

  2. Step 2: Compute selling price of each article

    First article at 20% profit → SP = 500 × 1.2 = ₹600. Second article at 10% loss → SP = 500 × 0.9 = ₹450.

  3. Step 3: Sum selling prices

    Total SP = 600 + 450 = ₹1,050.

  4. Step 4: Find overall profit amount and percent

    Profit = Total SP - Total CP = 1,050 - 1,000 = ₹50. Profit % = (50 ÷ 1,000) × 100 = 5%.

  5. Final Answer:

    5% profit → Option A

  6. Quick Check:

    Total CP = 1,000; Total SP = 1,050 → SP > CP → Profit ✅

Quick Variations

1. Different CPs but equal quantities.

2. Same CP but varying profit and loss percentages.

3. Weighted average cases when quantities are different.

Trick to Always Use

  • Step 1: Always calculate Total CP and Total SP.
  • Step 2: Compare → If SP > CP → Profit; If CP > SP → Loss.
  • Step 3: Overall % = (Difference ÷ Total CP) × 100.

Summary

Summary

  • Always compute total Cost Price (CP) and total Selling Price (SP) before concluding.
  • Overall profit/loss % = (Total SP - Total CP) ÷ Total CP × 100 - do not average percentages.
  • When quantities differ, use weighted aggregation (sum CPs and SPs across items).
  • Quick verification: if Total SP > Total CP → profit; if Total SP < Total CP → loss.

Example to remember:
Two items each CP ₹500 → SPs ₹600 and ₹450 → Total CP ₹1,000, Total SP ₹1,050 → 5% overall profit.

Practice

(1/5)
1. A shopkeeper buys 2 articles at ₹400 each. He sells the first at 20% profit and the second at 10% loss. Find the overall profit or loss percent.
easy
A. 5% profit
B. 2% profit
C. 5% loss
D. 2% loss

Solution

  1. Step 1: Compute total cost price

    Total CP = 400 + 400 = 800.

  2. Step 2: Calculate individual selling prices

    SP1 = 400 × 1.2 = 480; SP2 = 400 × 0.9 = 360.

  3. Step 3: Compute total selling price

    Total SP = 480 + 360 = 840.

  4. Step 4: Determine profit or loss

    Profit = 840 - 800 = 40.

  5. Step 5: Compute profit percentage

    Profit % = (40 ÷ 800) × 100 = 5%.

  6. Final Answer:

    5% profit → Option A

  7. Quick Check:

    Total CP = 800, SP = 840 → Profit confirmed ✅
Hint: Always add SPs and CPs, then compare.
Common Mistakes: Averaging 20% and -10% directly.
2. A person buys 3 articles at ₹200 each. He sells one at 10% profit, another at 20% profit, and the third at 10% loss. Find the overall profit percent.
easy
A. 5%
B. 6.67%
C. 7.5%
D. 8%

Solution

  1. Step 1: Compute total cost price

    Total CP = 200 × 3 = 600.

  2. Step 2: Calculate individual selling prices

    SP1 = 200 × 1.1 = 220; SP2 = 200 × 1.2 = 240; SP3 = 200 × 0.9 = 180.

  3. Step 3: Compute total selling price

    Total SP = 220 + 240 + 180 = 640.

  4. Step 4: Determine total profit

    Profit = 640 - 600 = 40.

  5. Step 5: Compute profit percentage

    Profit % = (40 ÷ 600) × 100 = 6.67%.

  6. Final Answer:

    6.67% profit → Option B

  7. Quick Check:

    SP > CP → Profit confirmed ✅
Hint: Add total SP - total CP to find profit/loss.
Common Mistakes: Taking direct average (10+20-10)/3 = 6.67% by chance only works if CPs equal.
3. A trader buys 2 articles, one for ₹600 and another for ₹400. He sells both at 10% profit. Find the overall profit percent.
easy
A. 8%
B. 9%
C. 10%
D. 11%

Solution

  1. Step 1: Compute total cost price

    Total CP = 600 + 400 = 1,000.

  2. Step 2: Calculate individual selling prices

    SP1 = 600 × 1.1 = 660; SP2 = 400 × 1.1 = 440.

  3. Step 3: Compute total selling price

    Total SP = 660 + 440 = 1,100.

  4. Step 4: Determine profit

    Profit = 1,100 - 1,000 = 100.

  5. Step 5: Compute profit percentage

    Profit % = (100 ÷ 1,000) × 100 = 10%.

  6. Final Answer:

    10% profit → Option C

  7. Quick Check:

    Both sold at 10% gain → total must be 10% ✅
Hint: If same % used for all, overall % = same.
Common Mistakes: Overcomplicating calculation.
4. A trader buys 5 articles at ₹100 each. He sells 3 at 20% profit and 2 at 10% loss. Find the overall profit or loss percent.
medium
A. 8% profit
B. 4% profit
C. 5% profit
D. 2% loss

Solution

  1. Step 1: Compute total cost price

    Total CP = 100 × 5 = 500.

  2. Step 2: Calculate selling prices for sub-groups

    SP of 3 = 3 × (100 × 1.2) = 360. SP of 2 = 2 × (100 × 0.9) = 180.

  3. Step 3: Compute total selling price

    Total SP = 360 + 180 = 540.

  4. Step 4: Determine profit

    Profit = 540 - 500 = 40.

  5. Step 5: Compute profit percentage

    Profit % = (40 ÷ 500) × 100 = 8%.

  6. Final Answer:

    8% profit → Option A

  7. Quick Check:

    Total SP 540 > Total CP 500 → Profit confirmed ✅
Hint: Compute CP vs SP carefully.
Common Mistakes: Averaging directly.
5. A person buys 4 articles at ₹250 each. He sells 2 at 10% profit and 2 at 20% profit. Find the overall profit percent.
medium
A. 12.5%
B. 13%
C. 15%
D. 20%

Solution

  1. Step 1: Compute total cost price

    Total CP = 250 × 4 = 1,000.

  2. Step 2: Calculate selling prices for groups

    SP of 2 = 2 × (250 × 1.1) = 550. SP of other 2 = 2 × (250 × 1.2) = 600.

  3. Step 3: Compute total selling price

    Total SP = 550 + 600 = 1,150.

  4. Step 4: Determine profit

    Profit = 1,150 - 1,000 = 150.

  5. Step 5: Compute profit percentage

    Profit % = (150 ÷ 1,000) × 100 = 15%.

  6. Final Answer:

    15% profit → Option C

  7. Quick Check:

    Total CP 1,000 → SP 1,150 → Profit = 150 ✅
Hint: Weighted average using CP.
Common Mistakes: Just averaging 10% and 20% as 15% without checking CP.

Mock Test

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