Commodity X rises by 40 paise per year and Y by 15 paise per year. In 2001, X cost Rs. 4.20 and Y cost Rs. 6.30. In which year will X cost 40 paise more than Y?

Problem restatementX and Y increase linearly each year. Find the year when X = Y + Rs. 0.40.

Given data

• In 2001: X₀ = Rs. 4.20; Y₀ = Rs. 6.30
• Annual increases: ΔX = Rs. 0.40; ΔY = Rs. 0.15

Concept/ApproachLet n = number of years after 2001. Write linear expressions for prices and impose X = Y + 0.40.

Step-by-step calculationX = 4.20 + 0.40nY = 6.30 + 0.15nCondition: 4.20 + 0.40n = 6.30 + 0.15n + 0.400.25n = 2.50 ⇒ n = 10Year = 2001 + 10 = 2011

Verification/AlternativeIn 2011: X = 4.20 + 10×0.40 = 8.20; Y = 6.30 + 10×0.15 = 7.80; indeed X − Y = 0.40.

Common pitfallsSetting X = Y (ignoring the +0.40), or using rupees/paise inconsistently.

Final Answer2011