# Thread: Percentage question but I don't get it!!

1. ## Percentage question but I don't get it!!

Ranjit started work in 2003.
In 2004 he moved to a different job and his pay decreased by 15%
At the end of each of the years 2004 and 2005 he was given an increase in pay. The percentage increase in pay was the same each time.
Ranjit worked out that he was now paid 22.4% more than he was paid in 2003.
Calculate the percentage increase that he received at the end of 2004 and 2005.

Can anyone help me???

2. Originally Posted by Bauer_rules
Ranjit started work in 2003.
In 2004 he moved to a different job and his pay decreased by 15%
At the end of each of the years 2004 and 2005 he was given an increase in pay. The percentage increase in pay was the same each time.
Ranjit worked out that he was now paid 22.4% more than he was paid in 2003.
Calculate the percentage increase that he received at the end of 2004 and 2005.

Can anyone help me???
Do it step by step. Let X be his pay in 2003. "In 2004 he moved to a different job and his pay decreased by 15%". Okay, in 2004 he made X- 0.15X= 0.85X.

"At the end of each of the years 2004 and 2005 he was given an increase in pay. The percentage increase in pay was the same each time."
Call the percentage increase (written as a decimal of course) be A A "percent" of his salary is 0.85XA so his new salary is 0.85X+ 0.85XA= 0.85X(1+A). The next year we do the same thing except now we multiply A by 0.85X(1+A) to find the increase so his new salary, after the second increase, is 0.85X(1+A)^2

"Ranjit worked out that he was now paid 22.4% more than he was paid in 2003" so we have 0.85X(1+ A)^2= X+ .224X= 1.224X.

We can divide both sides of the equation by X to get 0.85(1+ A)^2= 1.224.
(1+ A)^2= 1.224/0.85= 1.44. Taking the square root of that 1+ A= 1.2 so A= .2. His percentage pay increase was 20%.

### percentage question in 2003

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