PERCENTAGES
Percentages is the most important for all the examinations. The importance of ‘Percentages’ is accentuated by the fact that there are a lot of questions related to the use of percentage in all chapter of commercial arithmetic. In Data Interpretation at least 80% of the total calculation is based on the addition and percentage.
Definition
The concept of percentage mainly applies to ratios and the percentage value of ratio is arrived at by multiplying by 100 the decimal value of the ratio. For example, a student score 20 marks out of 30 marks. His percentage can be calculated;
(20/30) (100) = 66.66%
Percent in its simplest form means per cent i.e. per hundred
Per cent – Per hundred
40% = (40/100) – 2/5 = 0.4
(Note – to remove %, we divide by 100 and to converts into %, we multiply by 100)
Contents
• Base value
• Percentage change
• Change of base
• Successive percentage change
• Multiplying factor
Basic formula of percentage
P% of a number(N) = (P/N) * N
Ex. What is the 40% of 300?
= (40/100) * 300 = 120
Ex. What percent of 270 of 90?
= (90/270) * 100 = 33.33%
Base value
One of the most critical aspects of the percentage is the denominator, which in other words is also called the base value of the percentage. No percentage value calculated without knowing the base to which the percentage is to be calculated.
Let’s say India won 60% of matches out of 200
= (60 or 0.6) * (Base value)
In above question 200 is the base value
Percentage change
Percentage change = (FV - IV) / IV * 100
FV = Final value
IV = Initial value
Percentage change = (Increase-Decrease)/IV * 100
Likewise,
Percentage Error = (EV - CV) / CV * 100
EV = Error Value
CV = Correct Value
Ex. The production of a company increase from 80mn to 120mn units. What is the percentage increase in the production?
= (120-80) / 80 * 100 = 50%
Product stability Ratio
Applicable in a relationship where product of two quantities is to be maintained constant
• Speed * Time = Distance
• Price * consumption = Expenditure
• Length * Breadth = Area
In general A * B = constant
If A is increase by some certain percentage, then B is required to be decrease by some certain percentage so product remain constant.
Successive Percentage change
Whenever there are successive changes on a particular base, the net change can be can be expressed as a single percentage
a + b (ab / 100)
ex. If the price of petrol increases successively by 20% and then by 10% then the net change in percentage change
= 20% + 10% + (20 * 10) / 100
= 32%
Multiplying Factor
A is the 50% of B
A= (50 / 100) * 100 = 0.5B
Which also means, A is 50% less then B
Similarly
A is 50% more than B
A = B + (50 / 100) * B = 1.5B
Which also means, A is 150% of B
In general,
Multiplying factor = 1 + (R / 100)
Percentage using multiplying factor
Final value = initial value (1 + R / 100)
Multiplying Factor = (FV / IV)
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