Question

A number is increased by $20\%$ and then decreased by $20\%$, the final value of the number is?

एक संख्या में $20\%$ की वृद्धि हुई है और फिर $20\%$ की कमी हुई है, संख्या का अंतिम मान कितना होगा?

• A. Increase by 5%
  
  5% की वृद्धि
• B. Decrease by 5%
  
  5% की कमी
• C. Increase by 4%
  
  4% की वृद्धि
• D. Decrease by 4%
  
  4% की कमी

Answer 1

The correct option is D Decrease by 4%


4% की कमी
Let the number be $100.$

First it is increased by $20\%,$ then the new value

$=100+20\%$ of $100$

$=100+\frac{20}{100}\times 100$

$=100+20=120$

Now, the resulting new number is decreased by $20\%,$ then the final value

$=120-20\%$ of $120$

$=120-\frac{20}{100}\times 120$

$=120-24=96$

Percentage change in the final value in comparison to the original one

$=\frac{\text{Change in value}}{\text{Original value}}\times 100\%$

$=\frac{96-100}{100}\times 100=-4\%$