Assignment:
In 1990, a price index based on 1980 = 100 had a value of z. During 1990, it was rebased at 1990 = 100, and in 1998 the new index stood at 112.
If the total price movement between 1980 and 1998 was an increase of 40%, was was the value of z in 1990, that is, before rebasing?
The answer given was,
Using ratios, 1.12 x (z/100) = 1.40, giving z = 125.
Q1. Why did 40% get changed to 1.40, why not 0.40? Where does the one come from?
Q2. Why is the left had side of the equation 1.12 x (z/100) and not 1.12 + (z/100).
Q3. Can you recommend any books so I can learn about this type of question and how the underlying algebra works.
Provide complete and step by step solution for the question and show calculations and use formulas.