Shortcuts in Quantitative Aptitude for Competitive Exams – Percentage
The word “per cent” is derived from the latin words “per centum”, which • means “per hundred”.
A percentage is a fraction with denominator hundred.
It is denoted by the symbol %.
Numerator of the fraction is called the rate per cent.
VALUE OF PERCENTAGE
Value of percentage always depends on the quantity to which it refers.
Consider the statement :
“65% of the students in this class are boys”. From the context, it is understood that boys form 65% of the total number of students in the class. To know the value of 65% of the total number of students in the class, the value of the total number of boys student should be known.
If the total number of students is 200, then, the number of boys
NOTE: that the expressions 6%, 63%, 72%, 155% etc. do not have any value to themselves. Their values depend on the quantities to which they refer.
Some Quick Results:
To express the fraction equivalent to % :
Express the fraction with the denominator 100, then the numerator is the answer
EXPRESSING ONE QUANTITY AS A PER CENT WITH RESPECT TO OTHER
To express a quantity as a per cent with respect to other quantity following formula is used.
Note : To apply this formula, both the quantities must be in same unit.
PERCENTAGE INCREASE OR DECREASE OF A VALUE
When a number x is increased or decreased byy%, then the new number 100 ± y
- ‘+’ sign is used in case of increase.
- ‘ – ‘ sign is used in case of decrease.
- If A’s income is r % more than that of B, then B’s income is less than that of A by
- If A’s income is r % less than that of B, then B’s income is more than that of A by
- if A is x% of C and B is y% of C,then A is x 100% of B.
- x % of a quantity is taken by the first, y % of the remaining is taken by the second and z % of the remaining is taken by third person. Now, if A is left in the fund, then the initial amount
- x % of a quantity is added. Again, y % of the increased quantity’ is added. Again z % of the increased quantity is added. Now it becomes A, then the initial amount
- If the value of a number is first increased by a% and later decreased by a%, then the net effect is always a decrease which is equal to a% of a and is written as
- If the price of a commodity increases by r %, then reduction in consumption, so as not to increase the expenditure is
- If the price of a commodity decreases by r %, then the increase in consumption so as not to decrease the expenditure is
- If due to r% decrease in the price of an item, a person can buy A kg more in x, then
1. If the original population of a town is P, and the annual increase
is r %, then the population after n years is
and population before n years
2. If the annual decrease be r %, then the population after n years is
Population before n years
First Increase and then decrease :
1. If the value is first increased by x % and then decreased by y % then there is % increase or decrease, according to
the + ve or – ve sign obtained respectively.
2. Average percentage rate of change over a period
Successive increase or decrease
If the value is increased successively by x % and y % then the final increase is given by
If the value is decreased successively by x % and y % then the final decrease is given by
Student and Marks
- The percentage of passing marks in an examination is x%. If a candidate who scores y marks fails by z marks, then the maximum marks of M
- A candidate scoring x % in an examination fails by ‘a’ marks, while another candidate who scores y% marks gets ‘b’ marks more than the minimum required passing marks. Then the maximum marks
- If two candidates contested in an election and one candidate got x % of total votes and still lose by y votes, then
- Total number of votes casted
2-dimensional figure and area
- If the sides of a triangle, square, rhombus or radius of a circle are increased by a%, its area is increased by