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Successive Profit & Loss

Introduction

In aptitude exams, sometimes articles are sold through successive transactions, where a profit or loss is made more than once on the same item. For example: a shopkeeper first sells an article to another trader at a profit, and that trader sells it again at another profit/loss.

These problems cannot be solved by directly adding/subtracting percentages. Instead, we apply a specific formula for successive percentages.

Pattern: Successive Profit & Loss

Pattern

If a profit/loss of x% is followed by a profit/loss of y%, the net effect is:

Net % = x + y + (x × y) / 100

Here, treat profit as positive (+) and loss as negative (-). Final result > 0 → Net profit. Final result < 0 → Net loss.

Step-by-Step Example

Question

A trader sells an article at a profit of 20%, and the next buyer sells it again at a loss of 10%. Find the overall profit or loss percentage.

Options:

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

Solution

  1. Step 1: Identify the successive changes.

    Successive changes are +20% (profit) and -10% (loss).

  2. Step 2: Apply the successive-percentage formula.

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

  3. Step 3: Interpret the result.

    Positive result → 8% overall profit.

  4. Final Answer:

    8% overall profit → Option A

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

    Assume CP = 100 → after +20% = 120 → after -10% = 120 - 12 = 108 → Net = 108 - 100 = 8 → 8% profit ✅

Quick Variations

Case 1: Two successive profits (say +10% and +20%). Net % = 10 + 20 + (10×20)/100 = 32% profit.

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

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

Trick to Always Use

  • Use formula: Net % = x + y + (x×y)/100.
  • Assign positive for profit, negative for loss.
  • If unsure, assume CP = 100 and calculate step by step.
  • Quickly identify: Positive = Profit, Negative = Loss.

Summary

Summary

  • Use the successive-percentage formula: Net % = x + y + (x×y)/100.
  • Assign + for profits and - for losses before applying the formula.
  • Verify results by assuming CP = 100 and computing successive SP values.
  • Interpret sign: positive → overall profit; negative → overall loss.

Example to remember:
+20% followed by -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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