Shortcut formula for countinous percentage change..

  Some important formula on percentage.

let x is original/initial term , y is final term and p,q,r are the continuous percentage changes 

Or you can say

x changes in y after getting p%,q%,r% changes which can be increment or decrement.


In increment case :

1. Final value, y=x((100+p)(100+q)(100+r))/100*100*100


2. Original or initial value ( you can remember formula by using the trick that in all the words original, initial and denominator letter i is coming p,q,r Will be in denominator)

x=y*100*100*100/(100+p)(100+q)(100+r)

In decrement case just replace the + sign with - sign .


3. Final value, y=x((100-p)(100-q)(100-r))/100*100*100

4. Initial value, x=y*100*100*100/(100+p)(100+q)(100+r)

x or y will be in numerator in all cases.  


There are many types of question based on this formula . These are given below :

1. A man loses 15 % of his money an after spending 85% of the remainder he is left with 510. how much had he at first? 
solution.  
Here we have to find original value. so percentage changes will be in denominator.
and changes are negative so - will be used.  

hence initial value=510*100*100/(100-15)(100-85)

answer=4000.


2. if the annual increase in the population of a town be 2% and the present population be 65025 what was it two years ago?
sol.
* initial value
* increment

 initial population = 65025*100*100/(100+2)(100+2)

ans= 62500.

3.The manufacturer of an article makes a profit of 5%,the wholesale dealer makes profit of 10% and retailer makes a profit of 15 % . if retailer sold it for 5313 then manufacturing price was .

solution.

*initial price
* profit

initial price=5313*100*100*100/(100+5)(100+10)(100+15)


ans. 4000


4.If the initial price is 100. There is first  increment of 5% , then decrement of 10% and then again increment of 15% then what will be final price?
solution.

*final price
*inc* Dec* inc

final price=100*(100+5)(100-10)(100+15)/100*100*100

ans. 108.67