Shortcut of Percentage-2

Shortcut 26:
Net change in percentage for continuous increase or decrease

[latex]F.V=\frac{100+a}{100}\times\frac{100+b}{100}\times\frac{100+c}{100}\times I.V [/latex]

a, b, c = values of percentage increase or decrease.
Substitute ‘-‘ if it is 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?
Answer:
a = +10
b = -20
c = +30
Substitute the values in the above formula, we get
F.V = (11/10)(8/10)(13/10) x 30000
= 34320

Shortcut 27:
Percentage increase and decrease are same

[latex](a^2/100)\%decrease[/latex]

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 = 102/100 = 1% decrease.
New price of watch = 1000 – (1/100)1000
= 1000 – 10
= 990
New price of watch = Rs. 990

Shortcut 28:

Steady increase or decrease

                  [latex]\;F.V=I.V\lbrack1+(a/100)\rbrack^n[/latex]               

a = percentage increase or decrease
Substitute ‘-‘ before ‘a’ if it is percentage decrease
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
I.V = 200000
Substitute the values in the above equation, we get
F.V = 200000[1.1]3
F.V = 266200
Population of the city after three years = 266200

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