An online business sells two varieties of cat food, 'standard' and 'luxury'. It

orders these from its supplier each October for the year ahesad. The data for

$2021$ and $2022$ are displayed in Table $1.$

Table $1$

$($a$)$ Calculate the $($chained$)$ price index for $2022,$ taking $2021$ as the base

year.

$($b$)$ The RPI for October $2021$ was $312\mathrm{.}0,$ and the RPI for October $2022$

was $356\mathrm{.}2.$ Use this information, together with your calculation

from $($a$),$ to compare the change in cat food prices with the overall

change in this period.

$($c$)$ An RPI index$-$linked pension was $E450$ per month in October $2021.$

How much should the pension be per month in October $2022?$ Give

your answer rounded to the nearest pound.

$($d$)$ Calculate the purchasing power of the pound in October $2022$ compared

with October $20121.$ Give your answer rounded to the nesarest penny.