PERCENTAGE
Percent :-The meaning of the term percent is ‘for every hundred’.
It can be defined as follows:
“A percent is a fraction whose denominator is 100 and the numerator of the fraction is called the rate percent.” percent is denoted by the sing %.
Some Formula to solve question.
Formula 1 If we have to find y% of x, then
y% of x = x × y/100
Formula 2
Expressing percent (x%) into fraction.
Required fraction = x/100
Formula 3
Expressing a fraction = ( x/y) percent
Required percentage =( x/y ×100)%
formula 4
To find how much percent one quantity is of another.
Required percentage = (The quantity to be expressed in percent)/(2nd quantity (in respect of which the percent has to be obtained))×100
Mind it? For this formula, both quantities must be in same unit.
formula 5
(i) If x is a% more than y, then y is less than x by
(a/(100+a)×100) %
(ii)If x is a% less than y, then y is more than x by
(a/(100¬-a)×100) %
Formula 6
It the valueof number is 1st increased by a% and later decreased by a%, then the net effect is always a decrease
which is equal to a2% and a and is written as
a^2/(100 )% or (a/10)^2%
Formula 7
When the value of object is first changed (increased or decreased) by a% and then changed (increased or decreased) by b%, then
Net Effect = [±a±b+(±a)(±b)/100]%
Net effect is increased or decreased according to the +ve and -ve sign, respectively.
Formula 8
If the population of a town is P and it increases (or decreases) at the rate of R% per annum, then
(i) Population, after n year = P (1±R/100)^n
(ii)Population, n year ago = P/(1±R/100)^n
Mind it? Use ‘+’ sign for increment and ‘-’ sign for decrement.
SOLVED EXAMPLES
Ex.1. Calculate 20% of 5500.
(a) 1000 (b) 1200 (c) 1300 (d) 1100
Sol. 20/100×5500=1100
Ex.2: 210 is what % of 1500
(a) 15% (b) 16% (c) 14% (d) 20%
Sol. 210/1500×100=14%
Ex.3: What is the value of 72 % of two-fifth of 450?
(1) 648.4 (2) 129.6 (3) 324.2 (4) 162.6 (5) None of these
Sol 72% of 2/5 of 450
=72/100 × 180 = 129.6
Ex.4: Last year Ajay planted 170 mango trees. He increased the number by 40% this year. How many mango trees will he plant this years?
(1) 248 (2) 228 (3) 238 (4) 328 (5) None of these
Sol.: Required number of trees = (170×140)/100 = 238
Ex.5: Surjeet Singh’s salary is 80% of Ranjeet’s salary and 120% of Latika’s salary. What is Surjeet Singh’s salary
if Ranjeet’s salary is Rs. 15,000 ?
(1) Rs. 10, 000 (2) Rs. 18, 000 (3) Rs. 12,500
(4) Rs. 10,500 (5) None of these
Sol.: Surjeet’s Salary = (1500×80)/100 = Rs. 12000
