Concept of Percent Change

Percent Change

Here base is x

Percentage Change (increase or decrease) in a quantity,
p% = $\frac{Changeinquantity}{Originalquantity}$ × 100% = $\frac{y-x}{x}$ × 100%

Q. If price of sugar increases from Rs 18/kg to Rs 30/kg, then what is the percent increase?

Explanation:

Change in price = 30 – 18 = Rs 12 (Plus sign denotes an increase)
So, Percent change = $\frac{Changeinquantity}{Originalquantity}$ × 100%
= ($\frac{12}{18}$ × 100)% = ($\frac{2}{3}$ × 100)% = 66.67%
(Plus sign denotes a percentage increase)

Q. If price of sugar decreases from Rs 25/kg to Rs 15/kg, then what is the percent decrease?

Explanation:

Change in price = 15 – 25 = Rs -10 (Minus sign denotes a decrease)
So, Percent change = $\frac{Changeinquantity}{Originalquantity}$ × 100%
= ($\frac{-10}{25}$ × 100)% = ($\frac{-2}{5}$ × 100)% = -40%
(Minus sign denotes a percentage decrease)

Finding new quantity

When a quantity x is increased/decreased by p%, then:

New quantity, y = Base ± Absolute change in Base
= x ± p% of x = x ± x(p/100) = x (1 ± p/100)

Concept of Multiplying Factor

New quantity, y = x ± p% of x = x (1 ± p%)

So, Multiplying factor : (1 ± p%)

• Multiplying Factor is the same as (1 + p/100) for p% increase
  E.g. Multiplying Factor for 15% increase = 1.15
  Multiplying Factor for 8% increase = 1.08
  

• Multiplying Factor is the same as (1 - p/100) for p% decrease
  Multiplying Factor for 35% decrease = 0.65
  Multiplying Factor for 5% decrease = 0.95
  

Q. If 60 is increased by 25%, find the new number.

Explanations :
1 2

Q. If 60 is decreased by 25%, find the new number.

Explanations :
1 2

Q. By how much percent is 36 more than 27?

Explanations :
1 2

Q. By how much percent is 40 less than 60?

Explanations :
1 2

Q. Two numbers are 12.5% and 25% more than a third number respectively. The first number must be how much percent more/less than the second number?

Explanation :