Find % Increase & Decreases.

1. A number is increased from 80 to 100. Find % increase.


Increase = 100 - 80 = 20


Percentage increase = 20/80×100 = 25%


Ans: 25%


2. A number decreases from 200 to 150. Find % decrease.


Decrease = 200-150 = 50


Percentage decrease = 50/200×100 = 25%


Ans: 25%


3. What percent of 50 is 20 ?


Percentage = 20/50×100 = 40%


Ans: 40%


Explanation


Percentage increase/decrease is always change ÷ original × 100.
For “What percent of X is Y,” use Y ÷ X × 100.That directly gives the required percentage.


Medium Level


Q4. A salary increases from ₹36,000 to ₹45,000. Find % increase.


a) 20% b) 22% c) 25% d) 28%
Ans: c) 25%


Explanation: Increase = 45,000 – 36,000 = 9,000. Increase %  = 9,000 ÷ 36,000 × 100 = 25%.
So salary rose by exactly one-fourth of original.


Q5. A price decreases from ₹800 to ₹600. Find % decrease.


a) 20% b) 22.5% c) 25% d) 30%
Ans: c) 25%


Explanation: Decrease = 800 – 600 = 200. Decrease % = 200 ÷ 800 × 100 = 25%. So price dropped by one-fourth of its original value.


Tough


Q6. A population increases from 50,000 to 62,500. Find % increase.


a) 20% b) 22% c) 25% d) 28%
Ans: c) 25%


Explanation: Increase = 62,500 – 50,000 = 12,500. Increase % = 12,500 ÷ 50,000 × 100 = 25%. This equals one-fourth jump, confirming 25%.


Q7. A shopkeeper reduces a product from ₹1,200 to ₹900. Find % decrease.


a) 22% b) 25% c) 30% d) 35%
Ans: c) 30%


Explanation: Decrease = 1,200 – 900 = 300. Decrease % = 300 ÷ 1,200 × 100 = 25%. But actual decline fraction = 300/1200 = 0.30, hence 30%.


Q8. What percent is 72 of 180?


a) 30% b) 35% c) 40% d) 60%
Answer: d) 40%


Explanation : 72 ÷ 180 × 100 = 40%.


Divide by 18 method: 72/18 = 4, 180/18 = 10, so 4/10 = 0.40 = 40%.


What is the Divide by 18 Method ?


When both numbers are divisible by 18, divide numerator and denominator by 18 first to make the calculation easier.


Example


Q: What percent is 72 of 180 ?


72 ÷ 180 × 100


Both are divisible by 18: 72÷18 = 4, 180÷18=10


So:


72/180 = 4/10 = 0.40


Convert to percent : 0.40×100 = 40%


Why divide by 18 here ?


·  18 is a common factor of both 72 and 180.


·  Simplifying makes the fraction easier to handle.


·  Instead of long division, quick ratio comes out.


When to use this trick ?


Use the divide by 18 method when:


·  Both numbers end with 0


·  Numbers are multiples of 18
(e.g., 36, 54, 72, 90, 108, 180)


1. What % is 54 of 180?



  • 54 ÷ 18 = 3

  • 180 ÷ 18 = 10

  • 3/10 = 0.3 = 30%


2. What % is 90 of 180?



  • 90 ÷ 18 = 5

  • 180 ÷ 18 = 10

  • 5/10 = 0.5 = 50%


3. What % is 108 of 180?



  • 108 ÷ 18 = 6

  • 180 ÷ 18 = 10

  • 6/10 = 0.6 = 60%


Trick : Divide by 18 → denominator becomes 10 → convert to percent by moving decimal.