Percentage

1. Basic Percentage Calculations

Formula: (Part / Total) × 100 = Percentage

• Example 1: What is 25% of 600?
  Solution: (25/100) × 600 = 150
• Example 2 (RRB NTPC 2020): 15% of a number is 90. Find the number.
  Solution: 15% of x = 90 ⇒ (15/100)x = 90 ⇒ x = (90 × 100) / 15 = 600

2. Percentage Increase & Decrease

Formula: [(Change / Original) × 100]

• Example 1: A value increases from 200 to 250. What is the % increase?
  Solution: Increase = 250 - 200 = 50 ⇒ (50/200) × 100 = 25%
• Example 2 (SSC CGL 2022): A value increases by 20% and then decreases by 20%. Find the net change.
  Solution: Net % Change = 20 - 20 - (20×20)/100 = -4% ⇒ Net decrease of 4%

3. Marks & Exam Questions

Commonly asked in SSC CHSL, CGL, and HSSC.

• Example 1 (SSC CHSL 2019): A student scored 30% and failed by 20 marks. Passing marks are 40%. Find total marks.
  Solution: Let total marks = x
  40% of x - 30% of x = 20 ⇒ 10% of x = 20 ⇒ x = 200
• Example 2: A student gets 360 out of 600 marks. What is the percentage?
  Solution: (360/600) × 100 = 60%

4. Successive Percentage Change

Formula: A + B + (AB/100)

• Example 1: A value is increased by 10% and again by 20%. What is total % increase?
  Solution: 10 + 20 + (10×20)/100 = 32%
• Example 2 (HSSC 2021): A population grows by 5% annually for 2 years. Find net % increase.
  Solution: 5 + 5 + (5×5)/100 = 10.25%

5. Profit, Loss & Discount (Using Percentages)

Often comes in SSC CGL, RRB Group D

• Example 1 (RRB Group D 2018): CP = ₹100, marked up by 40%, discount = 10%. Find profit%.
  Solution: MP = ₹140, SP = 140 - 10% of 140 = ₹126 ⇒ Profit = 26%
• Example 2: A man buys a pen for ₹80 and sells it at ₹100. Find profit %.
  Solution: Profit = 20 ⇒ (20/80) × 100 = 25%

6. Discount (Single & Successive)

• Example 1: A product marked ₹500 is sold at 20% discount. What is the selling price?
  Solution: SP = 500 - 20% of 500 = ₹400
• Example 2: Two successive discounts of 10% and 20% on ₹1000.
  Solution: After 1st: 1000 - 100 = 900; After 2nd: 900 - 180 = ₹720

7. Data Interpretation (DI)

Used heavily in SSC, Railways DI sections

• Example: In a pie chart, sales of Product A is 20%. If total sales = ₹1,00,000, find sales of A.
  Solution: 20% of 100000 = ₹20,000

Tips to Remember

• 25% = 1/4, 50% = 1/2, 75% = 3/4 – know key conversions
• Successive % shortcut: A + B + AB/100
• In exams, always look to simplify using ratios

50 Previous Year Questions – Percentage (With Solutions)

• SSC CGL 2022: If 40% of a number is 280, what is the number?
  Options: A) 600 B) 700 C) 800 D) 900
  Solution: Let the number be x. 40% of x = 280 → (40/100) × x = 280 → x = (280 × 100)/40 = 700. Answer: B) 700
• RRB NTPC 2020: A number is increased by 20% and then decreased by 20%. What is the net percentage change?
  Options: A) 4% increase B) 4% decrease C) No change D) 2% decrease
  Solution: Net % change = 20 - 20 - (20×20)/100 = -4%. Answer: B) 4% decrease
• HSSC 2021: A student scores 30% and fails by 15 marks. If he had scored 50%, he would have passed by 5 marks. What are the passing marks?
  Options: A) 40 B) 35 C) 30 D) 50
  Solution: Difference in % = 50% - 30% = 20% Difference in marks = 15 + 5 = 20 marks So, 20% = 20 ⇒ Total marks = 100 Passing marks = 30% of 100 + 15 = 45 Answer: Not listed – correct answer: 45
• SSC CHSL 2019: If 25% of a number is 300, what is the number?
  Options: A) 1200 B) 1000 C) 1400 D) 1500
  Solution: 25% = 300 → Number = (300 × 100)/25 = 1200 Answer: A) 1200
• RRB Group D 2018: 10% of a number is 150. What is 40% of the number?
  Options: A) 600 B) 750 C) 550 D) 500
  Solution: Number = (150 × 100)/10 = 1500 40% of 1500 = (40/100) × 1500 = 600 Answer: A) 600
• SSC CGL 2020: A price is increased by 25%. By how much percent should it be decreased to get the original price?
  Options: A) 20% B) 25% C) 15% D) 30%
  Solution: Let original price = 100 → New = 125 Let x% decrease gives back 100 → (100 - x)% of 125 = 100 ⇒ (125 × (100 - x))/100 = 100 ⇒ 12500 - 125x = 10000 ⇒ 125x = 2500 ⇒ x = 20% Answer: A) 20%
• SSC CGL 2022: If 40% of a number is 280, what is the number?
  Options: A) 600 B) 700 C) 800 D) 900
  Solution: Let the number be x. 40% of x = 280 → (40/100) × x = 280 → x = (280 × 100)/40 = 700.
  Answer: B) 700
• RRB NTPC 2020: A number is increased by 20% and then decreased by 20%. What is the net percentage change?
  Options: A) 4% increase B) 4% decrease C) No change D) 2% decrease
  Solution: Net % change = 20 - 20 - (20×20)/100 = -4%.
  Answer: B) 4% decrease
• HSSC 2021: A student scores 30% and fails by 15 marks. If he had scored 50%, he would have passed by 5 marks. What are the passing marks?
  Options: A) 40 B) 35 C) 30 D) 50
  Solution: Difference in % = 50% - 30% = 20%
  Difference in marks = 15 + 5 = 20 marks
  So, 20% = 20 ⇒ Total marks = 100
  Passing marks = 30% of 100 + 15 = 45.
  Answer: Not listed – correct answer: 45
• SSC CHSL 2019: If 25% of a number is 300, what is the number?
  Options: A) 1200 B) 1000 C) 1400 D) 1500
  Solution: 25% = 300 → Number = (300 × 100)/25 = 1200.
  Answer: A) 1200
• RRB Group D 2018: 10% of a number is 150. What is 40% of the number?
  Options: A) 600 B) 750 C) 550 D) 500
  Solution: Number = (150 × 100)/10 = 1500
  40% of 1500 = (40/100) × 1500 = 600.
  Answer: A) 600
• SSC CGL 2020: A price is increased by 25%. By how much percent should it be decreased to get the original price?
  Options: A) 20% B) 25% C) 15% D) 30%
  Solution: Let original price = 100 → New = 125
  Let x% decrease gives back 100 →
  (100 - x)% of 125 = 100 ⇒ (125 × (100 - x))/100 = 100
  ⇒ 12500 - 125x = 10000 ⇒ 125x = 2500 ⇒ x = 20%.
  Answer: A) 20%
• RRB NTPC 2019: A man spends 80% of his income. His income is ₹45,000. What is his savings?
  Options: A) ₹9000 B) ₹9500 C) ₹8000 D) ₹7500
  Solution: Savings = 20% of ₹45,000 = ₹9000.
  Answer: A) ₹9000
• HSSC 2022: Population increases by 10% annually. Find population after 2 years if current is 10,000.
  Options: A) 12100 B) 12000 C) 11000 D) 10000
  Solution: Population after 1 year = 10,000 × 1.10 = 11,000
  Population after 2 years = 11,000 × 1.10 = 12,100.
  Answer: A) 12100
• SSC CGL 2021: A value decreases by 20% and again by 20%. Find net % decrease.
  Options: A) 36% B) 40% C) 32% D) 28%
  Solution: Net % decrease = 20 + 20 + (20×20)/100 = 36%.
  Answer: A) 36%