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Overall Profit/Loss (Multiple Articles)

Introduction

कई real-world problems में अलग-अलग articles को अलग-अलग profit या loss पर खरीदा और बेचा जाता है। Overall profit या loss निकालने के लिए Total Cost Price (CP) और Total Selling Price (SP) का सही comparison करना जरूरी होता है।

यह pattern important है क्योंकि यह सिखाता है कि multiple items के results को कैसे combine किया जाए, न कि हर item को अलग-अलग treat किया जाए।

Pattern: Overall Profit/Loss (Multiple Articles)

Pattern

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

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

Step-by-Step Example

Question

एक shopkeeper 2 articles खरीदता है, दोनों का CP ₹500 है। वह एक को 20% profit पर बेचता है और दूसरे को 10% loss पर। Overall profit या loss percent ज्ञात करें।

Options:

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

Solution

  1. Step 1: Calculate total cost price

    पहले article का CP = ₹500, दूसरे का CP = ₹500. Total CP = 500 + 500 = ₹1,000.

  2. Step 2: Compute selling price of each article

    पहला article 20% profit पर → SP = 500 × 1.2 = ₹600. दूसरा article 10% loss पर → 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. अलग-अलग CPs लेकिन equal quantities।

2. Same CP लेकिन अलग profit और loss percentages।

3. Quantities अलग हों तो weighted average method (Total CP और Total SP का sum) उपयोग करें।

Trick to Always Use

  • Step 1: हमेशा Total CP और Total SP निकालें।
  • Step 2: Compare करें → SP > CP → Profit; CP > SP → Loss।
  • Step 3: Overall % = (Difference ÷ Total CP) × 100.

Summary

Summary

  • Conclusion निकालने से पहले हमेशा total Cost Price (CP) और total Selling Price (SP) निकालें।
  • Overall profit/loss % = (Total SP - Total CP) ÷ Total CP × 100 - percentages को average न करें।
  • Quantities अलग होने पर weighted aggregation करें (CPs और SPs को जोड़ें)।
  • Quick check: यदि Total SP > Total CP → profit; यदि Total SP < Total CP → loss।

याद रखने योग्य उदाहरण:
दो items: CP ₹500-₹500 → SP ₹600 और ₹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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