Inflation rate (IR) is the average increase in cost or price of goods over a period of time. If something costs x and the rate is r% for the year, the same item a year later costs (1+(r/100))x. The house price index HPI (h) is a number directly proportional to the average rate of change of property prices over a period of time. So if a house price is H in one year and the next year it is H+y, y=kh, where k is the constant of proportionality, so the new price is H+kh.
If 1.5% is tripled it becomes 4.5%, so r=4.5%. A house price of H would be inflated to 1.045H, so kh=0.045.
If r=1.5%=0.015, we know from the table that h=85 in 1996, and in 1997 r=1.6% when h=99, so we should be able to find k.
85k=0.015 or 99k=0.016 if the HPI is only affected by IR, because H goes from H to H+kh=H(1+(r/100)). Therefore, k=0.015/85=3/17000=0.00018, or k=0.016/99=0.00016. These values are different, but it's not clear whether the statement that HPI is only affected by IR applies to the whole HPI table or just to 1996. If we assume the latter, then we take k=0.00018; otherwise we use average k=0.00017. Let's see what difference it makes. For 1996 at triple r, 0.00018h=0.045, making h=0.045/0.00018=250. Using k=0.00017, 0.00017h=0.045, so h=264 and k=0.00016, h=281. These would apply at the beginning of 1997.
The HPI for 1997 (start of year) would be 250 outside the capital, if for 1996 the inflation rate had been 4.5%.