Successive Profit and Loss questions become simple when you stop adding percentages directly and start tracking how the base changes after every step. A 20% increase followed by a 10% decrease is not a 10% increase, because the second percentage is applied to a new value.
This guide focuses on multiplier logic, net percentage change, repeated profit or loss, successive discounts and reverse recovery questions commonly used in SSC, Banking and Railway arithmetic.
1. Why Successive Percentages Cannot Usually Be Added
Suppose a value starts at 100. After a 20% increase it becomes 120. A 10% decrease is now calculated on 120, not on the original 100.
Final value = 120 × 0.90 = 108.
So the net result is an 8% increase, not 10%.
2. Multiplier Method for Successive Changes
Convert every percentage change into a multiplier:
- 20% increase → 1.20
- 10% increase → 1.10
- 20% decrease → 0.80
- 15% decrease → 0.85
Final Value = Original Value × First Multiplier × Second Multiplier
This is the safest general method because it works for increases, decreases, profits, losses and discounts.
3. Net Percentage Change Formula
For two successive percentage changes a% and b%:
Net change% = a + b + ab/100
Use a positive sign for an increase and a negative sign for a decrease.
Example: +20% followed by −10%:
20 − 10 − 2 = 8% increase.
4. Two Successive Increases
If a value increases by 10% and then by 20%:
Net change = 10 + 20 + 2 = 32% increase.
Multiplier check: 1.10 × 1.20 = 1.32.
So an original value of ₹500 becomes ₹660.
5. Increase Followed by Decrease
A 25% increase followed by a 20% decrease gives:
25 − 20 − 5 = 0%.
Multiplier check: 1.25 × 0.80 = 1.00.
This is a special case where the second decrease exactly reverses the first increase.
6. Equal Increase and Decrease Do Not Cancel
If a value increases by x% and then decreases by the same x%, the net result is always a loss:
Net loss% = x²/100
Example: +20% followed by −20%:
Net loss = 20²/100 = 4%.
Starting from 100: 100 → 120 → 96.
7. Successive Discounts
For discounts a% and b%:
Effective Discount% = a + b − ab/100
Example: 10% and 20% successive discounts:
10 + 20 − 2 = 28%.
On MP ₹2,000, final SP = 2,000 × 0.90 × 0.80 = ₹1,440.
For deeper MP-SP applications, study Discount and Marked Price Questions.
8. Successive Profit and Loss on a Transaction Value
If an amount rises by 20% and later falls by 10%, multiplier logic is still the same.
For ₹1,000:
1,000 × 1.20 × 0.90 = ₹1,080.
The net change is 8% increase.
The words profit and loss do not change the mathematics; what matters is the percentage base at each step.
9. Three or More Successive Changes
For three or more changes, multiplier method is safer than trying to extend a shortcut mentally.
Example: +20%, −10%, +25%:
Net factor = 1.20 × 0.90 × 1.25 = 1.35.
Therefore net result = 35% increase.
For repeated changes, multiply every factor in sequence.
10. Repeated Same Percentage Change
If the same percentage r% is applied n times:
Final factor = (1 ± r/100)n
Example: two successive 10% increases:
1.10² = 1.21, so net increase = 21%.
Two successive 10% decreases give 0.90² = 0.81, so net decrease = 19%.
11. Restore a Value After a Loss
A loss of x% requires a larger percentage gain to return to the original value.
Required gain% = x ÷ (100 − x) × 100
Example: after a 20% loss, value becomes 80% of original.
Required gain = 20/80 × 100 = 25%.
This is why a 20% loss followed by a 20% gain does not restore the original value.
12. Required Decrease After an Increase
If a value rises by x%, the percentage decrease required to return to the original value is:
Required decrease% = x ÷ (100 + x) × 100
Example: after a 25% increase, required decrease = 25/125 × 100 = 20%.
13. Ratio Shortcut for Reverse Recovery
After a 20% loss, new value : original value = 80:100 = 4:5. To return from 4 parts to 5 parts, the required increase is 1/4 = 25%.
Similarly, after a 25% increase, new : original = 5:4. Returning from 5 parts to 4 parts requires a 1/5 = 20% decrease.
For more ratio-based speed methods, see Profit and Loss Tricks for Faster Solving.
14. Common Successive-Change Mistakes
- Adding percentages directly: the base usually changes after the first step.
- Ignoring signs: treat decreases as negative in the net-change formula.
- Assuming equal gain and loss cancel: +x% and −x% produce x²/100 loss.
- Using the two-change shortcut for many stages: multiplier method is safer for three or more changes.
- Reversing a loss with the same gain: recovery percentage is calculated on the reduced value.
For a dedicated error-repair guide, use Common Profit and Loss Mistakes.
15. Solved Exam-Speed Examples
Example 1: +30% followed by −20% → 30 − 20 − 6 = 4% increase.
Example 2: −10% followed by −5% → effective decrease = 10 + 5 − 0.5 = 14.5%.
Example 3: +15% followed by +20% → 15 + 20 + 3 = 38% increase.
Example 4: −25% followed by +20% → −25 + 20 − 5 = 10% decrease.
16. Quick Practice Check
- Find the net change for +20% followed by +10%.
- Find the net change for +20% followed by −20%.
- Find the effective discount for 15% and 10% successive discounts.
- After a 25% loss, what percentage gain restores the original value?
- After a 20% increase, what percentage decrease restores the original value?
- Find the net effect of +20%, −10% and +25%.
Answers: (1) 32% increase; (2) 4% decrease; (3) 23.5%; (4) 33⅓%; (5) 16⅔%; (6) 35% increase.
17. Exam-Speed Decision Path
- Two changes only → signed net-change formula can be fast.
- Three or more changes → use multipliers.
- Equal increase and decrease → x²/100 loss shortcut.
- Two discounts → effective-discount formula.
- Return to original after loss/increase → use reverse recovery formula or ratio.
If the formulas themselves are unclear, revise Profit and Loss Formulas for Exams.
18. Next Step
Return to the Profit and Loss Master Guide for the complete chapter structure. If CP, SP and percentage base need revision, use Profit and Loss Basics.
For exam-style application, move to Exam-Based Profit and Loss Questions and then test mixed concepts in Profit and Loss Practice Set 1.