Price of a product increased

Question

If the price of a certain product is increased by 15 percent, by approximately what percent must the new price be reduced in order to obtain the original price?

Answer 1

Let P = original price

To increase by 15% means   P + (15/100)*P  = 1.15*P
The increased price is 1.15*P.

Now, to find the percentage decrease:

      what value do we multiply 1.1*P by, then subtract from P, in order to get P again ?
           P  =  1.15*P  -  X * 1.15*P
           P   =  1.15*P * (1-X)

           P / (1.15*P)  = 1-X

             X = 1 - P / (1.15*P)

              X = 1 - 1/1.15

               X = 13%      [rounded]

Answer 2

Let's say price of a product cost of $100 is raised by 15%. So the new price will be $115.

 

Now we are asked to reduce this $115 back to original price $100.

 

So we need to figure out what percentage of $115 is $15.

 

Can you figure it out that part?