Advanced Concept of Percentage Change

Advanced Concept of Percentage Change

(A) If a value p is increased by x%, then we have to decrease the resultant value by
 (x/x+100 x 100)% to get back to the original value p.

original value p ------------->  p * x /100 --------> ( p + px/100) = p (100 + x/100)

Now the percentage decrease

= (p(100 + x /100) - p) / p (100 + x/100 ) x 100 = ( x/100+ x  * 100) %

In other words (i.e., in terms of fraction) if a value is increased by n/d then to get back the same number p from the resultant value, we have to decrease the increased value by ( n/ d+n).

Example 1:

Salary of arun in 2001 was 100rs per day and his salary in 2002 was 125rs per day. Again in 2003 his salary was rs 100 per day.

i) what is the percentage increase in his salary in 2002?
ii) what is the percentage decrease in his salary in 2003 over 2002?

Solution:

i) 125 - 100 /100  x 100 = 25%

ii) 125 - 100/125 x 100 = 20%

In fact is same absolute change but percentage change is different due to different denominator (i.e., base change). So the base change is as much important as the numerator or absolute change in quantity.


Example 2: 

Age of arun is 20 years. If the udhay age is 25% greater than that of arun then how much per cent arun age is less than udhay age?

Solution:

Age of arun                                    age of udhay

20 -------------+25%------------------->     25
     <-------------(-20%)-----------------

Solution using percentage change formula
here x = 25, then

percentage decrease (or less)  =  25/125 x 100 =20%

Solution using fractional change formula

since increase = 1/4                        ( 25% = 1/4)

Therefore decrease = 1/4+1 = 1/5 = 20%


Example 3

Arun has 33.33% more pencils than udhay has. By how much per cennt less pencils udhay has than that of arun?

Solution:

arun --------33% = 1/3-------------------> udhay
        <------(-25% = 1/4 = 1/3+1 )--------------

so udhay has 25% less pencils than arun has.