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Successive Profit & Loss

Introduction

Aptitude exams में कभी-कभी किसी वस्तु को successive transactions में बेचा जाता है, जहाँ एक ही item पर एक से ज़्यादा बार profit या loss होता है। उदाहरण: पहले shopkeeper profit पर बेचता है, फिर अगला buyer उसे दोबारा profit/loss पर बेचता है।

ऐसे सवालों को सीधे percentage जोड़कर या घटाकर हल नहीं किया जा सकता। इसके लिए successive percentages का खास formula इस्तेमाल किया जाता है।

Pattern: Successive Profit & Loss

Pattern

अगर किसी वस्तु पर पहले x% का profit/loss हो और फिर y% का profit/loss हो, तो कुल असर होता है:

Net % = x + y + (x × y) / 100

यहाँ profit को + और loss को - मानें। Final result > 0 → Net profit. Final result < 0 → Net loss.

Step-by-Step Example

Question

एक व्यापारी किसी वस्तु को 20% profit पर बेचता है, और अगला buyer उसे दोबारा 10% loss पर बेचता है। कुल profit या loss प्रतिशत निकालें।

Options:

  • A. 8% overall profit
  • B. 10% overall profit
  • C. 6% overall profit
  • D. No profit, no loss

Solution

  1. Step 1: Successive changes पहचानें।

    Successive changes = +20% (profit) और -10% (loss) हैं।

  2. Step 2: Successive-percentage formula लगाएँ।

    Net % = 20 + (-10) + (20 × -10) / 100 = 20 - 10 - 2 = +8%.

  3. Step 3: Result को interpret करें।

    Result positive है → 8% overall profit.

  4. Final Answer:

    8% overall profit → Option A

  5. Step 4: Quick Check (CP = 100 लेकर verify करें).

    CP = 100 → +20% के बाद = 120 → फिर -10% = 120 - 12 = 108 → Net = 108 - 100 = 8 → 8% profit ✅

Quick Variations

Case 1: दो successive profits (+10% और +20%). Net % = 10 + 20 + (10×20)/100 = 32% profit.

Case 2: दो successive losses (-10% और -20%). Net % = -10 - 20 + (-10×-20)/100 = -28% (net loss).

Case 3: एक profit, एक loss (+25%, -20%). Net % = 25 - 20 + (25×-20)/100 = 25 - 20 - 5 = 0 → No overall gain/loss.

Trick to Always Use

  • Formula इस्तेमाल करें: Net % = x + y + (x×y)/100.
  • Profit के लिए + और loss के लिए - sign लगाएँ।
  • अगर doubt हो, CP = 100 मानकर step-by-step calculate करें।
  • Sign देख कर जल्दी पहचानें: Positive = Profit, Negative = Loss.

Summary

Summary

  • Successive percentage का formula: Net % = x + y + (x×y)/100.
  • Profit को + और Loss को - लेकर formula में substitute करें।
  • Result verify करने के लिए CP = 100 method बहुत आसान है।
  • Sign के आधार पर final result निकालें: positive → profit, negative → loss.

याद रखें:
+20% और -10% → Net % = 20 - 10 + (20×-10)/100 = 8% profit

Practice

(1/5)
1. A shopkeeper gains 10% on one article and again 20% on reselling it. Find the overall gain percentage.
easy
A. 30%
B. 32%
C. 28%
D. 25%

Solution

  1. Step 1: Identify both profit percentages.

    Gains = +10% and +20%.

  2. Step 2: Apply successive percentage formula.

    Net % = 10 + 20 + (10 × 20)/100 = 30 + 2 = 32%.

  3. Final Answer:

    32% profit → Option B

  4. Quick Check:

    Assume CP = 100 → After +10% = 110 → After +20% = 132 → Profit = 32% ✅
Hint: Use Net % = x + y + (x×y)/100.
Common Mistakes: Simply adding 10% + 20% = 30% without the product term.
2. An article is sold at a loss of 15% and then again at a loss of 10%. Find the overall loss percentage.
easy
A. 25%
B. 26.5%
C. 23.5%
D. 24%

Solution

  1. Step 1: Identify both losses.

    Losses = -15% and -10%.

  2. Step 2: Apply successive percentage formula.

    Net % = -15 - 10 + (-15 × -10)/100 = -25 + 1.5 = -23.5%.

  3. Final Answer:

    23.5% loss → Option C

  4. Quick Check:

    CP = 100 → After -15% = 85 → After -10% = 76.5 → Loss = 23.5% ✅
Hint: Take loss as negative in the formula.
Common Mistakes: Adding -15% and -10% directly = -25% without correction.
3. A trader sells at a profit of 25% and then at a loss of 20%. Find the overall result.
easy
A. 5% profit
B. 2% loss
C. 0% (no gain, no loss)
D. 6% profit

Solution

  1. Step 1: Identify profit and loss.

    Profit = +25%, Loss = -20%.

  2. Step 2: Apply successive change formula.

    Net % = 25 - 20 + (25 × -20)/100 = 5 - 5 = 0%.

  3. Final Answer:

    No profit, no loss → Option C

  4. Quick Check:

    CP = 100 → After +25% = 125 → After -20% = 100 → back to CP ✅
Hint: If net % = 0, then it’s no profit/loss.
Common Mistakes: Forgetting the product term and wrongly concluding profit or loss.
4. An article is first sold at 30% profit, then at 40% profit. Find the overall profit percentage.
medium
A. 70%
B. 82%
C. 60%
D. 72%

Solution

  1. Step 1: Identify profit percentages.

    Profits = +30% and +40%.

  2. Step 2: Apply successive percentage formula.

    Net % = 30 + 40 + (30 × 40)/100 = 70 + 12 = 82%.

  3. Final Answer:

    82% profit → Option B

  4. Quick Check:

    CP = 100 → After +30% = 130 → After +40% = 182 → Profit = 82% ✅
Hint: Always add x, y and their product/100.
Common Mistakes: Stopping at 30 + 40 = 70%, missing the product term.
5. A man sells a good at 12% profit and then again at 15% loss. Find the net result.
medium
A. 5% loss
B. 3% profit
C. 4.8% loss
D. 2% loss

Solution

  1. Step 1: Identify profit and loss.

    Profit = +12%, Loss = -15%.

  2. Step 2: Apply successive percentage formula.

    Net % = 12 - 15 + (12 × -15)/100 = -3 - 1.8 = -4.8%.

  3. Final Answer:

    4.8% loss → Option C

  4. Quick Check:

    CP = 100 → After +12% = 112 → After -15% = 95.2 → Loss = 4.8% ✅
Hint: Use Net % = x + y + (x×y)/100 with signs.
Common Mistakes: Adding +12 and -15 only = -3%, missing the correction factor.

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