In November 2020, India's oil basket price was 65$, WPI 2%, CPI 6.8%. In June 2021, India's oil basket was 70$, CPI almost the same 6.2%, but WPI soared to 12.2%. How is it possible? What can be the factors for a sudden increase in WPI when oil prices are almost the same and CPI is still the same?
Let's recall that inflation is usually computed as a year-on-year (annual) percentage change in the consumer price index. Therefore, CPI inflation for June 2021 will compare the CPI in June 2021 to the CPI in June 2020. Hence, inflation of say 6.2 percent (as you mentioned) means that the CPI in June 2021 was 6.2 percent higher when compared to CPI in June 2020. The same rationale holds for computing WPI inflation. The basic idea is that inflation is an annual percentage change in the relevant price index (CPI or WPI). When you are comparing crude oil prices, notice that you are comparing prices in November 2020 and June 2021 while the June 2021 WPI data you mentioned is an annual percentage change. For the purpose of calculating inflation, it will perhaps be suitable to compare crude oil prices in June 2021 to crude oil prices in June 2020 (so that the time period of the comparison is the same for inflation as well as for crude oil price). For data on the price of the Indian crude oil basket see https://www.ppac.gov.in/.
Furthermore, the WPI and the CPI are indices that are composed of many items, each having a weight in the index. Therefore, say a 5 percent increase in crude oil price will not necessarily lead to a 5 percent increase in inflation. The change in the price of other items will also have to be taken into account while calculating aggregate inflation. As such, the items in the WPI and CPI are different, and hence the inflation as shown by the two indices will be different.
Notwithstanding the unavailability of official June 2021 data for the CPI and the WPI, let us use WPI data for May 2021 to understand the trends. Annual WPI inflation was 12.9 percent in May 2021, out of which 2.5 percentage points were contributed by 'Primary Articles,' 3.4 percentage points by 'Fuel & Power,' and the remaining 7.0 percentage points by 'Manufactured Products.' In fact, since August 2020 'Manufactured Products' have accounted for the majority of the increase in the WPI. The increase in WPI inflation has been driven by a rapid increase in the prices of 'Manufactured Products,' although 'Primary Articles' and 'Fuel & Power' have also contributed to the increase.