Index Numbers Questions

Fisher's index number is the:

The index number for the price of diesel in $2015$ was $125$ and in $2016$ it was $140$, with $2011$ as the base year. What is the percent increase in the price of diesel from $2015$ to $2016$?

Consider the following statements regarding index numbers:(i) Simple average of price relative is a weighted index numbering method.(ii) The index number for the base year is always 100.(iii) If the price index is 25, then the prices have increased by 25%.(iv) If the price index is 75, then the prices have decreased by 25%.Which of the statements are correct?

Calculate the index number using the simple average of price relative method for the data below, taking 2010 as the base year:ItemPrice in 2010Price in 2015A100140B80120C160200D220385E112112

Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is $125$. Given:Prices in 1985: $75,85,\alpha ,100$ Prices in 1986: $90,115,75,\beta$ Find the value of $(4\beta -5\alpha )$.

If $\sum p_0{q}_0=160$, $\sum p_0{q}_1=250$, $\sum p_1{q}_0=200$ and $\sum p_1{q}_1=288$, then Fisher's ideal index number is:

The index number calculated for the data below by simple weighted aggregate method is 110.| Item | Price (Current) | Price (Base) | Weights || :--- | :--- | :--- | :--- || A | $p$ | 4 | 60 || B | 3 | 2 | $q$ || C | 2 | 3 | 40 |Given $60p+3q=360$, then the value of $p$ will be: