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Percentage Increase/Decrease

Introduction

Percentage वाले बहुत common questions तब आते हैं जब किसी value को किसी निश्चित प्रतिशत से increase या decrease किया जाता है। ये questions exams में और real life (prices, population, salaries आदि) में बहुत दिखते हैं।

तरीका simple है: original value को (1 ± percentage/100) से multiply करें।

Pattern: Percentage Increase/Decrease

Pattern

मुख्य idea: New value = Original value × (1 + x/100) increase के लिए।

New value = Original value × (1 - x/100) decrease के लिए।

Sentence को math में बदलकर direct apply करें।

Step-by-Step Example

Question

किसी shirt की price ₹200 है। इसे 10% बढ़ा दिया जाता है। नई price निकालें।

Solution

  1. Step 1: Original value और % change लिखें।

    Sentence: Original price = 200, Increase = 10%.

  2. Step 2: Formula apply करें।

    Sentence: New value = Original × (1 + x/100).
    Math: New price = 200 × (1 + 10/100)

  3. Step 3: Simplify करें।

    New price = 200 × (1 + 0.10) = 200 × 1.10 = 220

  4. Step 4: Final Answer.

    Shirt की नई price = ₹220

  5. Step 5: Quick Check.

    200 का 10% = 20 → 200 + 20 = 220 ✅

Question

किसी town की population 50,000 है। यह 5% कम हो जाती है। नई population निकालें।

Solution

  1. Step 1: Original value और % change लिखें।

    Sentence: Original population = 50,000, Decrease = 5%.

  2. Step 2: Formula apply करें।

    Sentence: New value = Original × (1 - x/100).
    Math: New population = 50,000 × (1 - 5/100)

  3. Step 3: Simplify करें।

    New population = 50,000 × (1 - 0.05) = 50,000 × 0.95 = 47,500

  4. Step 4: Final Answer.

    नई population = 47,500

  5. Step 5: Quick Check.

    50,000 का 5% = 2,500 → 50,000 - 2,500 = 47,500 ✅

Quick Variations

अगर price x% बढ़े और फिर y% घटे: Step-by-step apply करें, या बाद में successive % change formula use कर सकते हैं।

अगर reverse में % change पूछा हो: जैसे: “Price 200 से 220 हुई → Increase = (20 ÷ 200) × 100 = 10%”.

Trick to Always Use

  • Step 1: Original value और % change लिखें।
  • Step 2: Increase के लिए multiplier: (1 + x/100), decrease के लिए: (1 - x/100)।
  • Step 3: Multiply करके simplify करें।
  • Step 4: Quick check के लिए original का x% add/subtract करें।

Summary

Summary

Percentage Increase/Decrease pattern इस तरह solve होता है:

  • Increase: New = Original × (1 + x/100)
  • Decrease: New = Original × (1 - x/100)
  • Quick check: Original का x% add या subtract करें।

इस method से increase/decrease वाले questions बहुत जल्दी और accurately solve होते हैं।

Practice

(1/5)
1. The price of a shirt is ₹200. It is increased by 10%. What is the new price?
easy
A. ₹220
B. ₹215
C. ₹210
D. ₹225

Solution

  1. Step 1: Identify original price and increase

    Original price = 200, Increase = 10%.

  2. Step 2: Apply increase multiplier

    New price = 200 × (1 + 10/100).

  3. Step 3: Compute the value

    200 × 1.10 = 220.

  4. Final Answer:

    ₹220 → Option A

  5. Quick Check:

    10% of 200 = 20 → 200 + 20 = 220 ✅
Hint: Increase → multiply by (1 + x/100).
Common Mistakes: Adding a fixed amount (e.g., ₹10) instead of the percentage.
2. The population of a town is 50,000. It decreases by 5%. What is the new population?
easy
A. 47,000
B. 47,500
C. 48,000
D. 47,250

Solution

  1. Step 1: Identify original value and decrease

    Original population = 50,000; Decrease = 5%.

  2. Step 2: Apply decrease multiplier

    New = 50000 × (1 - 5/100).

  3. Step 3: Compute the value

    50000 × 0.95 = 47,500.

  4. Final Answer:

    47,500 → Option B

  5. Quick Check:

    5% of 50000 = 2500 → 50000 - 2500 = 47500 ✅
Hint: Decrease → multiply by (1 - x/100).
Common Mistakes: Adding the percent instead of subtracting when decreasing.
3. The salary of a person is ₹40,000. It is increased by 15%. What is the new salary?
medium
A. ₹45,000
B. ₹46,500
C. ₹46,000
D. ₹44,000

Solution

  1. Step 1: Identify salary and increase

    Salary = 40,000; Increase = 15%.

  2. Step 2: Apply increase multiplier

    New salary = 40000 × (1 + 15/100).

  3. Step 3: Compute the value

    40000 × 1.15 = 46,000.

  4. Final Answer:

    ₹46,000 → Option C

  5. Quick Check:

    15% of 40000 = 6000 → 40000 + 6000 = 46000 ✅
Hint: Multiply by 1.15 for +15%.
Common Mistakes: Using 1.5 instead of 1.15 or miscalculating 15% of the base.
4. A company’s revenue was ₹800,000 last year. This year it decreased by 12%. What is the new revenue?
medium
A. ₹704,000
B. ₹720,000
C. ₹680,000
D. ₹700,000

Solution

  1. Step 1: Identify original revenue and decrease

    Original revenue = 800,000; Decrease = 12%.

  2. Step 2: Apply decrease multiplier

    New = 800000 × (1 - 12/100).

  3. Step 3: Compute the value

    800000 × 0.88 = 704,000.

  4. Final Answer:

    ₹704,000 → Option A

  5. Quick Check:

    12% of 800,000 = 96,000 → 800,000 - 96,000 = 704,000 ✅
Hint: Decrease by 12% → multiply by 0.88.
Common Mistakes: Forgetting to convert percent to decimal before multiplying.
5. The price of an article is ₹5,000. It is first increased by 20% and then decreased by 10%. What is the final price?
medium
A. ₹5,500
B. ₹5,600
C. ₹5,700
D. ₹5,400

Solution

  1. Step 1: Identify original price

    Original price = 5,000.

  2. Step 2: Apply the 20% increase

    After +20%: 5000 × 1.20 = 6,000.

  3. Step 3: Apply the 10% decrease

    Then -10%: 6000 × 0.90 = 5,400.

  4. Final Answer:

    ₹5,400 → Option D

  5. Quick Check:

    Net % = 20 - 10 - (20×10)/100 = 8% → 5000 × 1.08 = 5400 ✅
Hint: Apply multipliers stepwise: ×1.20 then ×0.90.
Common Mistakes: Assuming net change = 20% - 10% = 10% (incorrect).

Mock Test

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