the price of notebook increased by x% to bring the price of earlier level it had to be reduce by 50/3%.find the value of x
Answers
Let's understand this by Percentage change Graph (PCG).
100 -----(increase by 25%)----> 125 --------(decrease by 20%)-------> 100
Note: Change in % = ( (Final - Initial) / Initial) * 100 %
1st Case: ((125-100)/100) * 100% = 25 % (positive value, hence increase)
2nd case: ((100 -125)/125) * 100 % = -20 % (negative value, hence 20% decrease)
Your case:
100 ----(some % increase)---> Z -----(decrease by 16.66%)----> 100
First, You need to find what number drops by 16.66 % to become 100, i.e. value of Z.
Therefore, ((100-Z)/100) * 100 % = -16.66. Solve this, you will get, Z = 120.
Now, the situation is,
100 ------(increase by some %)-----> 120
Definitely, it's 20%
Explore the PCG. Look at the pic!
(100 + x) – (100 + x/100) x (50/3) = 100
(100 + x) [ 1 – 50/300 ] = 100
(100 + x) [ 300 – 50/300 ] = 100
(100 + x) [ 250/300 ] = 100
(100 + x) = 100 x 300/250
(100 + x) = 30000/250
(100 + x) = 120
x = 120 – 100
x = 20
Hence, The value of x = 20 or 20% Increase was made to the initial price.