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Some important formula of percentage
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Example: Income of Ram is 25% more than Shyam. Then find Shyam’s income how much percent less than Ram?
Answer:
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Example: In an examination, Geeta secured 20% less marks than Laxmi. Then marks secured by Laxmi is how much percent more than Geeta?
Answer:
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(iii) If a quantity is first increased by m% and then decreased by m% then net result will be always decreased and it will be equal to
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Example: The salary of a person first increased by 10% and then it is decreased by 10% again. Then what will be changed in his salary?
Answer:
The net salary will be decreased.
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(iv) If a quantity is first changed (increased or decreased) by m% and then again changed by (increased or decreased) by n% then
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(+) means increased
(-) means decreased
Net Change is an increase or decrease according to the sign.
Example 1:
The price of a material is first increased by 25% and then decreased by 30%. Find the net percent change in the final price of that material.
Answer:
At first increased by 25%
Then decreased by 30%
So, Net Percentage change
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Net percent change is negative. It means that now the price of that material is decreased.
So, the price of that material is decreased by 12.5%.
Example 2:
The length of a rectangle is increased by 5% and the breadth of that rectangle is decreased by 8%. Find the net change in area.
Answer:
Length increased by 5%
Breadth decreased by 8%
So, Net Percentage change
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Net Percentage is negative. It means that are will decrease.
So, the area will decrease by 3.4%.
(v) If the price of commodity increases by m% then to keep the expenditure consumption should be decreased by
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Example:
If the price of sugar increases by 16% then by how much percent a householder should decrease its consumption so that the expenditure remains the same on sugar?
Solution:
So, decrease percentage in consumption.
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(vi) If the price of the commodity decreases by m% then to keep the expenditure the same. Consumption should be increased by
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Example:
The price of pulse decreased by 20%. Then by how much percent a householder should increase its consumption so that the expenditure remains the same on the pulse?
Answer:
The increased percentage in pulse
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(vii) Population Concept:
Let the population of a town be x and it changes (increases or decreases) at the rate y% per annum.
Then,
(a) Population after 1 year
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(b) Population n years ago
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(+) → sign when population increases.
(-) sign when population decreases.
If there is an increase then change in population is
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If there is a decrease then change in population is
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Example:
# If the annual growth rate of a town in population by 10% and the present population be 10000. What will be the population after 3 years hence?
Answer:
Population after 3 years will be
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# Present population of a town is 17280. Population growth is 20%. What was the population 3years ago?
Answer:
Population 3 years ago was
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(viii) Value depreciation
If the present value of a machine box be x and it depreciates at the rate y% per annum.
Then,
(a) Value of machine after n years will be
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(b) Value of machine n years ago was
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Example:
The value of a Lathe machine depreciates at the rate of 20% per annum. If the cost of machine at present is Rs. 200000. Then what will be its worth after 2years?
Answer:
Present value = Rs. 200000
Depreciation = 20% per annum
Year = 2
So, its worth after 2 years will be
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We can also find the greatest and lowest value using percentage.
Example:
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Some tricks for fast calculation.
(i) Splitting
Example:
# 48 % of 172
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# 65% of 285
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(ii) Interchanging
Example:
# 85% of 37.5
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# 63% of 14.29
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