Quantitative Aptitude Percentage Tutorial (Study Material)
Quantitative Aptitude Percentage Tutorial (Study Material).The term ‘per cent’ means one out of a hundred. In mathematics percentages are used to describe parts of a whole – the whole being made up of a hundred equal parts. The percentage symbol % is used commonly to show that the number is a percentage, less commonly the abbreviation ‘pct’ may be used.
Percentages are used frequently in all walks of life. “30% increase in fuel prices this winter”, “20% off all shoes”, “79% of people in the UK have an Internet connection”, “50% extra free”.
Understanding percentages is a key skill that will potentially save you time, money and make you more employable.
The word ‘per cent’ means per hundred. Thus, 19 per cent means, 19 parts out of 100 parts. This can also 19/100′
Therefore, per cent is a fraction whose denominator is 100. and the numerator of this fraction is called the rate percent. So, 19/100 = 19 percent. Here 19% is the rate. The sign for percent is %.
Fraction to Rate Per Cent
To convert (or express) any fraction a/b to rate per cent, multiply it by 100 and put a(%) sign.
a/b – fraction
a/b x 100% – rate percent
Example : Express 3/4 in rate per cent
Required rate per cent = 3/4 x 100% = 75 %
Rate Per Cent to Fraction
To convert a rate percent to a fraction, divide it by 100 and delete the % sign.
Example: 8% can be converted to a fraction as 8/100
Rate Per Cent of a Number
Rate per cent of a number is a product of equivalent fraction ( of rate percent ) and the number.
P% of A =(P/100) xA
Example: To find out 25% of 500
Solution: Required value = 25% of 500
= (25/100) x 500 ( 25/100 is equivalent fraction for 25%)
Relation Among Rate Per cent ,Number and Value
Let us consider a number. A’.
Then N is considered as the base over which value of different rate per cents are found out.
10% of N =10/100 x N =N/10 (value)
25% of N = 25/100 x N = N/4 (Value)
and so on.
Therefore, it is found that as the rate per cent changes, its related value for the same number will also change.
Conversely, different values stand for different rate per cents of the same number. As in the above example, N/10 stands tor 10% of N; stands for 25% of N and so on.
In the above context, a very useful relation is derived as:
any value/ its rate % of number = number (base)
Example: 9% of what number is 36?
Solution: Using the relation I.
the required number (base number) = 36/9% = 36/9 x 100 = 400
Note: Here. 36 is die value and its rale % of base number = 9%
Expressing a Given Quantity as a Percentage of Another Given Quality
Let one given quantity be A and another given quantity be y. It is often asked to find what percentage of y is A*. Here both quantities (A and y) should be in same units. If not, they should be converted into the same unit.
The question requires us to express one given quantity ‘x’ as a percentage of another given quantity y Since y is the basis of comparison, so, y will be in the denominator. But x is to be converted as percentage of y, hence x will be in the numerator of the fraction. Now to convert the fraction to percentage, we will multiply it by 100. So, we get
the required percentage = x/y x 100%.
Example: To find 30 is what per cent of 150’ or what percentage of 150 is 30 ?
Solution: Using the earlier concept, we find here that 150 is the basis of comparison and hence 150 will be in the denominator.
the required percentage = 30/150 x 100 = 20 %
Converting a Percentage into Decimals
Let the percentage be a positive integer, then place a decimal point after two places from the extreme right of the integer to convert it into a decimal. If the percentage is a single digit number, add one zero to the left of it and then place the decimal point for its conversion. % Sign is removed after conversion.
Example: 67% may be converted into decimals as 0.67. because 67% = 67/100= 0.67
8 % may be written as 0.08
2.53% is equivalent to 2.53
Let the percentage be a decimal fraction
The percentage being a decimal fraction, shift decimal by two places to the left. Add zero to the left of the fraction, if needed.
Let the percentage be a fraction
If the percentage is fraction of the form a/b then convert it into a decimal fraction and then follow the rule detailed in case II
Example: 1/4 % is equivalent to 0.25% which may be converted into decimals as 0.0025
Converting a Decimal into a Percentage
In this case, the method of 5.6 is reversed, i.e. shift the decimal point two places to the right. Add zero to the extreme right if required. Then add % sign.
Effect of Percentage Change on Any Quantity
Two Step Change of Percentage For a Number
In the first step, a number is changed (increased or decreased) by x%, and in the second step, this changed number is again changed (increased or decreased) by y%. then net percentage change on the original number can be conveniently found out by using the following formula.
net % change = x+y+ (xy/100)
If x or y indicates decrease in percentage, then put a (-) ve sign before x or y, otherwise positive sign remains.
Example: If a number is increased by 12% and then decreased by 18%, then find the net percentage change in the number.
Using the formula
net % change = x+y+(xy/100)
where x =12 y = -18
net % change = 12-18 + (12) x (-18)/100
=-6 – 2.16
(-) sign signifies that there is percentage decrease in the result. Therefore -8.16 indicates net 8.16% decrease of the given number as a result of 12% increase and 18% decrease.
It also implies that 12% increase and 18% decrease are equivalent to 8.16% decrease.
Percentage Change and its Effect on Product
- % effect on expenditure, when rate and consumption are changed, since rate x consumption = expenditure [A x B = product)
- % effect on area of rectanglc/squarc/triangle/circle, when its sides/radius are changed, since
Side1/Side2, = area, or radius x radius = area [A x B = product)
- % effect on distance covered, when time and speed are changed, since time x speed = distance. [A x B = product]
Rate Change and Change in Quantity Available for Fixed Expenditure
% Excess or % Shortness