Hey, it's a little late, but I can explain it if you're still interested.
We are given that the base year is 100 (the generic base year we use when we've no previous data with which to compare the CPI).
We know that the inflation rate is calculated at [CPI(Year 1) - CPI (Base year)]/CPI (Base Year)
Once we have the inflation of each separate basket of goods, we multiply each by their respective weighting factor and compare.
So for food, inflation = (110-100)/100 = 0.1
Multiplying by weighting factor of 30 gives an inflationary contribution of 3.0
For health, = (130-100)/100 = 0.3 * 10 = 3.0
Housing = (125-100)/100 = 0.25 * 15 = 3.75
Clothing = (120-100)/100 = 0.2 * 20 = 4.0
Comparing these figures we see that with 4.0, clothing has the largest figure and as such contributes most to the inflation rate of the economy.
I hope this clarified the problem for you.
