**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