Math percentage question

Question

the length of two rods are in the ratio of 2:9. The longer rod is reduced by 50% in length. What % must the shorter rod be increased to so that their ratio in length becomes 1:1

Answer 1

Let L be the total length of both rods.

 

2X + 9X = L

 

11X = L

 

X = L/11

 

The longer rod is (9/11)L

The shorter rod is (2/11)L

 

The longer rod is reduced by 50%, so the new length is (1/2)(9/11)L = (9/22)L

 

The formula for percent change is (new # - old #)/old#.

 

The shorter rod must be increased to (9/22)L from (2/11)L

new # = 9/22, old # = 2/11

 

percent change is:

new - old      9/22 - 2/11       9/22 - 4/22

-----------     ------------- = -------------------

  old                  2/11               2/11

 

5/22 divided by 2/11  = 5/22 * 11/2 = 5/4 = 1.25 = 125%

 

CHECK:

 

    2/11 * 5/4 = 10/44 = 5/22

 

  (2/11)L + (5/22)L = ((4/22)+(5/22))L = 9/22L which is half the length of the longer rod.

 

The shorter rod must be increased by 125% or 5/4