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Shortcut 23:

\(\%=\frac{{\mathrm V}_\mathrm c}{{\mathrm V}_\mathrm b}\times100 \)

Vc = Value to be compared
Vb = 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:
Vc = 1102
Vb = 1200
Percentage = (1102/1200) x 100
= 91.83%

Shortcut 24:

Percentage increase or decrease

\( \%=\frac{\mathrm F.\mathrm V\sim\mathrm I.\mathrm V}{\mathrm I.\mathrm V}\times100\)

F.V = Final value; I.V = Initial value
If final value is less than initial value, it is % decrease
If final value is more than initial value, it is % increase.
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:
F.V = 45000; I.V = 40000.
Substituting the values in the above formula, we get
% increase = [(45000 – 40000)/40000] x 100
= (5000/40000)x 100
= 12.5 % increase

Shortcut 25:

Net change in percentage after two individual percentage changes

\( \%=a+b+\frac{ab}{100}\)

a = first percentage change
b = second percentage change
Substitute ‘-‘ in case of percentage decrease
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