Question

In 1998, rice was selling at an average price of Rs. 120 per 20 kg, silk at Rs. 20 per metre, flat rent at Rs. 300 per flat and miscellaneous items at Rs. 100 per unit. By 2017, price of rice increased to Rs. 180 per 20 kg, flat rent to Rs. 450 and miscellaneous items by 100%. Using relative prices, index number of the year 2017 against the base year of 1998 was 160. By how much did the silk increase in price during the period?

• A. Rs. 10 per metre
• B. Rs. 8 per metre
• C. Rs. 3 per metre
• D. None of the above

Answer 1

The correct option is B

Rs. 8 per metre

Let the increase in price of silk be k.

$\begin{array}{cccc}\text{Item}& \text{Price in 1998 (P0)}& \text{Price in 2017 (P1)}& \text{Price Relative}(\frac{P1}{P0}\ast 100)\\ \text{Rice}& 120& 180& \left(\frac{180}{120}\right)\ast 100=150\\ \text{Silk}& 20& k& \left(\frac{k}{20}\right)\ast 100=5k\\ \text{Flat rent}& 300& 450& \left(\frac{450}{300}\right)\ast 100=150\\ \text{Miscellaneous}& 100& 200& \left(\frac{200}{100}\right)\ast 100=200\\ Total& & & 500+5k\end{array}$

$P01=\frac{\sum \left(\frac{P1}{P0}\right)\ast 100}{n}=\frac{500+5k}{4}=160500+5k=640\Rightarrow 5k=140$
k = Rs. 28

Hence, the increase in silk’s price = 28 - 20 = Rs. 8 per metre.