Shortcut – Percentage
Percentage Calculation
%=Value to be compared/Value to which it has to be compared * 100
$V_{c}$ = Value to be compared
$V_{b} $= Value to which it has to be compared, base value.
Question:
What is the percentage of marks scored by Sai in final exam, if she has scored 1102 out of 1200?
Answer:$V_{c} = 1102$
$V_{b} = 1200$
Percentage = (1102/1200) x 100
= 91.83%
Question:
Out of 65000 population, men are 39000. What is the percentage of women?
Answer:Women = 65000 – 39000 = 26000
Percentage of women = (26000/65000) x 100
= (2/5) 100 = 40 %
Shortcut – Percentage
Percentage increase or decrease: Percentage change =$\dfrac{From - To}{From} \times 100$
From – the value from which the change is happening
To – the value to which the change has happened.
If From value is less than To value, it is % increase
If From value is more than To value, it is % decrease.
Question:
Sradha’s monthly salary is Rs. 40000. If an increment of Rs. 5000 is provided, what is the percentage increase in her salary?
Answer:From = 40000;
To = 45000.
Substituting the values in the above formula, we get
% increase = [(45000 – 40000)/40000] x 100
= (5000/40000)x 100
= 12.5 % increase
Shortcut – Percentage
Net change in percentage when two changes are made.
a = first percentage change
b = second percentage change
Question:
Salary of Sai was Rs. 20000. If the salary is decreased by 10 percent and then increased by 30 percent, what is the new salary of Sai?
Answer:a = -10
b = 30
Net change = -10 + 30 + [(-10)(30)/100]
= 20 – 3 = +17% (positive value = % increase)
New salary of Sai
= 20000 + (17/100)20000
= 23400
Note:
If the net change value is negative, it means percentage decrease.
Shortcut – Percentage
Final value after multiple percentage changes.
(a, b and c) are the percentage changes.
The formula can be expanded or reduce according to the number of changes
given in the question.
Substitute ‘+’ for percentage increase.
Substitute ‘-‘for percentage decrease.
Question:
Salary of Shradha is Rs. 30000. It is increased by 10%, then decreased by 20% and again increased by 30%. What is her final salary?
a = +10;
b = -20;
c = +30
Substitute the values in the above formula, we get
Final Value
= (11/10)(8/10)(13/10) x 30000
= 34320
Shortcut – Percentage
Net percentage change when (a %) increase and (a %) decrease.
Net percentage change =$\dfrac{a^{2}}{100}% $decrease.
Question:
Price of a watch was Rs. 1000. The price is increased by 10% and then decreased by 10%. What is the price of the watch now?
Answer:a = 10
Net change in percentage =$ 10^{2}/100 $= 1% decrease.
New price of watch = 1000 – (1/100)1000
= 1000 – 10
= 990
Question:
Price of a product increased by 20% and the sales was reduced by 20%. By what percentage the income has reduced?
Answer:a = 20%
Percentage reduction in income
=$ 20^{2}/100$
= 4%
Shortcut – Percentage
Steady percentage increase or decrease.
a – steady rate of percentage increase or decrease.
Substitute ‘+’ for percentage increase.
Substitute ‘-‘for percentage decrease.
n – Number of times the percentage change occurs.
Question:
The population of a city is 200000. The population increases by 10% every year. What will be the population of the city after 3 years?
Answer:a = + 10
Initial Value = 200000
Substitute the values in the above equation, we get
Final Value = $200000[1.1]^{3}$
Final Value = 266200
Population of the city after three years
= 266200