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Successive Percentage Changes

Introduction

कई बार किसी value में percentage change एक से ज़्यादा बार होता है। उदाहरण: किसी price में एक साल 20% increase हो और अगले साल 10% decrease। ऐसे cases को successive percentage changes कहा जाता है।

यहाँ percentages को सीधे जोड़ना या घटाना सही नहीं होता। Net effect निकालने के लिए एक simple method use करते हैं।

Pattern: Successive Percentage Changes

Pattern

अगर किसी value में a% और फिर b% change होता है, तो net % change:

Net % = a + b + (a × b) / 100

Result positive हो तो net increase, negative हो तो net decrease।

Step-by-Step Example

Question

किसी price में पहले 20% increase और फिर 10% decrease होता है। Net percentage change निकालें।

Solution

  1. Step 1: Given changes लिखें।

    First increase = +20%, Second change = -10%

  2. Step 2: Formula apply करें।

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

  3. Step 3: Result समझें।

    Positive result मतलब Net increase of 8%।

  4. Step 4: Quick Check (100 method)।

    Start with 100.
    +20% → 120.
    -10% → 120 - 12 = 108.
    Net = 108 - 100 = +8% ✅

  5. Step 5: Final Answer.

    Net effect = 8% increase

Quick Variations

अगर दोनों increases हों: जैसे +10% और +20%. Net = 10 + 20 + (10×20)/100 = 32% increase.

अगर दोनों decreases हों: जैसे -10% और -20%. Net = -10 - 20 + (-10×-20)/100 = -28% (decrease)。

अगर increase के बाद decrease हो: जैसे +25%, -20%. Net = 25 - 20 - 5 = 0% (कोई change नहीं)。

Trick to Always Use

  • Formula: Net % = a + b + (a×b)/100.
  • + value = increase, - value = decrease।
  • Quick check के लिए हमेशा initial value = 100 मानकर changes apply करें।
  • Final value original से ज़्यादा है या कम - इसकी भी check कर लें।

Summary

Summary

Successive Percentage Change pattern, दो या ज़्यादा percentage changes के combined effect को निकालने में काम आता है।

Net % = a + b + (a × b) / 100

  • Increase के लिए positive, decrease के लिए negative sign use करें।
  • Result > 0 → net increase.
  • Result < 0 → net decrease.
  • 100 method से verify जरूर करें।

इसे अच्छे से समझने पर tricky exam questions भी जल्दी solve हो जाते हैं।

Practice

(1/5)
1. A price is increased by 10% and then decreased by 10%. What is the net percentage change?
easy
A. 1% decrease
B. 0%
C. 2% decrease
D. 1% increase

Solution

  1. Step 1: State the successive changes

    Given changes: +10% and -10%.

  2. Step 2: Use the successive % formula

    Net % = a + b + (a×b)/100 = 10 + (-10) + (10×-10)/100 = 0 - 1 = -1% → 1% decrease.

  3. Final Answer:

    1% decrease → Option A

  4. Quick Check:

    Start 100 → after +10% = 110 → after -10% = 99 → net decrease = 1% ✅
Hint: Use Net% = a + b + (a×b)/100.
Common Mistakes: Assuming +10% and -10% cancel out to 0% without using the product term.
2. The salary of a person is increased by 20% and then again increased by 10%. Find the net percentage increase.
easy
A. 30%
B. 32%
C. 31%
D. 28%

Solution

  1. Step 1: State the successive increases

    Given changes: +20% and +10%.

  2. Step 2: Apply the formula

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

  3. Final Answer:

    32% increase → Option B

  4. Quick Check:

    Start 100 → after +20% = 120 → after +10% = 132 → net increase = 32% ✅
Hint: Add the percentages and include (a×b)/100 term for successive increases.
Common Mistakes: Forgetting the (a×b)/100 term and giving 30% instead of 32%.
3. A shopkeeper increases the price of an item by 30% and then gives a discount of 20%. What is the net effect on price?
easy
A. 6% increase
B. 4% decrease
C. 2% increase
D. 4% increase

Solution

  1. Step 1: Identify successive change values

    Given changes: +30% and -20%.

  2. Step 2: Apply the net % formula

    Net % = 30 - 20 + (30×-20)/100 = 10 - 6 = 4% increase.

  3. Final Answer:

    4% increase → Option D

  4. Quick Check:

    Start 100 → after +30% = 130 → after -20% = 130 - 26 = 104 → net +4% ✅
Hint: Convert successive % to net using a + b + (a×b)/100; check with 100-method.
Common Mistakes: Ignoring the product term and reporting 10% instead of 4%.
4. A population decreases by 20% one year and increases by 25% the next year. What is the net percentage change?
medium
A. 5% increase
B. 0%
C. 2% decrease
D. 1% increase

Solution

  1. Step 1: Note the two changes

    Given changes: -20% and +25%.

  2. Step 2: Compute net % using formula

    Net % = -20 + 25 + (-20×25)/100 = 5 - 5 = 0% (no change).

  3. Final Answer:

    0% (no change) → Option B

  4. Quick Check:

    Start 100 → after -20% = 80 → after +25% = 100 → back to original ✅
Hint: Use the formula; many pairs cancel via the product term.
Common Mistakes: Adding -20 + 25 = 5% and assuming net +5% without the product term.
5. The price of sugar increased by 50% in one year and then decreased by 20% the next year. What is the net percentage change?
medium
A. 25% increase
B. 30% increase
C. 20% increase
D. 35% increase

Solution

  1. Step 1: State the successive changes

    Given changes: +50% and -20%.

  2. Step 2: Calculate net %

    Net % = 50 - 20 + (50×-20)/100 = 30 - 10 = 20% increase.

  3. Final Answer:

    20% increase → Option C

  4. Quick Check:

    Start 100 → after +50% = 150 → after -20% = 120 → net increase = 20% ✅
Hint: Compute net % using a + b + (a×b)/100 and keep track of signs.
Common Mistakes: Applying +50 - 20 = +30% incorrectly (misses -10% product correction).

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