"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%.