PERCENTAGE ( WITH EXPLANATION)

 PERCENTAGE ( WITH EXPLANATION)

  1.    Concept of percentage or Percentage formula

To express x% as a fraction: We have, x%
x/100 Thus, 30%=30/100= 3/10

In simple terms we can conclude that percentage symbol "%" means 1/100

In case we are having a fraction and we have to calculate its percentage then we will multiply it by 100.
that is, a/b=(a/b)×100)%

2.    Increase or decrease in percentage with price

(1) If the price of a commodity increases by R%, then the reduction in consumption -

 so as not to increase the expenditure will be = [R/ (100+R)×100]%

( 2) If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease-

 the expenditure will be = [R/(100−R)×100]

3.    Results on population
Formula's on result of population are very important when we have to calculate the population n years -

after or n years before,
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then
(1) Population after n years =P(1+R/100)ⁿ

(2)  Population before n years =P/(1+R/100)ⁿ

4.    Results on Depreciation
We know that value of a machine depreciate with time, so it will decrease with the time. 

      To calculate the value of machine after n years or before n years, we use these formula's

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum.
(1) Population after n years   = P(1−R/100)ⁿ

(2) Population before n years =P/(1−R/100)ⁿ

5.    Important results for Percentage
The formulas we are going to mention below is same as of increase or decrease in -

         consumption with increase or decrease in the commodity price, just here we are in a bit different context.
(1) If A is R% more than B, then B is less than A by = [R/(100+R)×100]%

(2) If A is R% less than B, then B is more than A by = [R/(100−R)×100]%

QUESTIONS :

1.    Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number-

  less than by the first

(1) 20%                 (2) 30 %

(3) 10%                 (4) 40%

2.    In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the-

 students failed in both the subjects, then find the percentage of students who passed in both the subjects.

(1) 40%                 (2) 41%

(3) 43%                 (4) 44%

3.    In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his-

      consumption so that his expenditure on it does not increase ?

(1) 20%                 (2) 30%

(3) 22%                 (4) 24%

4.    The value of a machine depreciates at the rate of 10% per annum. If its present is Rs.1,62,000.?

      What was the value of the machine 2 years ago ?

(1) 200000             (2) 20000

(3) 2000                 (4) None of these

5.    A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

(1) 60%                 (2) 62%

(3) 64%                 (4) 65%

 ANSWERS WITH EXPLANATIONS:

1.    (3) : Let the third number is x.
then first number = (100-30)% of x
= 70% of x = 7x/10

Second number is (63x/100)
Difference = 7x/10 - 63x/100 = 7x/10
So required percentage is, difference is what percent of first number
=> (7x/100 * 10/7x * 100 )% = 10%

2.    (4) : Failed in mathematics, n(A) = 34
Failed in English, n(B) = 42

n(AUB) = n(A) + n (B) – n (A∩ B )

= 34 + 42- 20 = 56
Failed in either or both subjects are 56

Percentage passed = (100−56)%=44%

3.    (1) : Reduction in consumption = [((R/(100+R))*100]%
? [(25/125)*100]%=20%.

4.    (1): Value of the machine 2 years ago
= Rs.[162000/(1-(10/100)²)]=Rs.[162000*(10/9)*(10/9)]= Rs.200000

5.    (3) : Let the number be x

Then, error =  (5/3)x – (3/5)x =(16/15)x

Error% = [(16x/15) /(5x/3)] * 100% = 64%