Final answer:
By calculating the difference in price increase rates between commodities X and Y starting from 2001 and solving for the year when X exceeds Y by 40 paise, we find that the year is 2011 (option B).
Step-by-step explanation:
The question asks in which year the price of commodity X will be 40 paise more than commodity Y given that the price of X increases by 40 paise per year and the price of Y by 15 paise per year, starting from 2001 where X was Rs.4.20 and Y was Rs.6.30. To solve this, let's denote the number of years after 2001 as 'n'. The price of X in the year 'n' after 2001 will be Rs.4.20 + (0.40 × n) and the price of Y will be Rs.6.30 + (0.15 × n).
We want to find when these prices satisfy the following condition: (Price of X) - (Price of Y) = Rs.0.40. By plugging in the given price functions, the equation becomes (4.20 + 0.40n) - (6.30 + 0.15n) = 0.40. Simplifying, the equation becomes 0.25n = 2.50, so n = 10. Thus, the year when the prices satisfy the condition will be 2001 + 10 = 2011.