Percentage is one of the most fundamental and frequently tested topics in quantitative aptitude. It is asked in almost every competitive exam including CAT, SSC CGL, SSC CHSL, Bank PO, Bank Clerk, Railway RRB and CSAT. A strong understanding of percentage concept, formulas and tricks is essential for scoring well in these exams. In this post we cover everything from the basic definition of percentage and rate percent, important percentage to fraction conversions, two-step successive percentage change formula, net percentage change formula for product of two variables and its applications on area, expenditure and distance — all explained with solved examples.
Percentage:- The word ‘per cent’ means per hundred. Thus 9 percent means 9 parts out of 100 parts. This can also be written as \(\frac{9}{100}\).
Therefore percentage is a fraction whose denominator is 100, and the numerator of this fraction is called the Rate Percent. So \(\frac{9}{100}\) = 9 per cent. The sign of percent is %.
Some Important Percentages and their equivalent Fraction
● To convert any fraction \(\frac{a}{b}\) into rate percent, multiply it by 100 and put a ‘%’ sign
\(\frac{a}{b} = \frac{a}{b} \times 100\% \)
ex. \(\frac{3}{4} = \frac{3}{4} \times 100\% = 75\% \)
● To convert a rate percent to a fraction, divide it by 100 and delete the ‘%’ sign.
ex. 5% = \(\frac{5}{100}\)
A% of B = \(\left(\frac{A}{100}\right) \times B\)
ex. 25% of 100 = \(\frac{25}{100} \times 100\) = 25
● How to understand a Percentage.
● Two step change of percentage of 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 found out by using the following formula:-
if x of y indicates decrease in percentage, then put a ‘-‘ sign before x or y, otherwise +ve sign will remains.
Percentage change & its effect on Product
If A is changed by x%, and also B is changed by y%, then the net percentage change of the product of A and B can be found out by the formula:-
if x or y indicates decrease in percentage, then put a -ve sign before x or y, otherwise +ve sign will remain.
⟶ % effect on expenditure, when rate and composition are changed, since rate × consumption = expenditure.
⟶ % effect on area of rectangle square/triangle/circle, when its side/radius are changed, since
side₁ × side₂ = area
or
radius × radius = area
⟶ % effect on distance converted, when time and speed are changed, since time × speed = distance
Example:- If length of a rectangle is increased by 20% and breadth is decreased by 30% then the % change in the area of the rectangle.
Solution:-
net % change in area = 20 – 30 + \(\frac{20 \times \left( – 30\right)}{100}\)
= -10 – 6
= -16%
So area will decrease by 16% Answer