The price of commodity X increases by Rs 60 every year, while the price of commodity Y increases by Rs 20 every year. If in 2002 the price of commodity X was Rs 320 and the price of commodity Y was Rs 740, in which future year will commodity X cost Rs 60 more than commodity Y?

Introduction / Context:
This is a typical arithmetic reasoning question involving linear growth in prices over time. Each commodity increases in price by a fixed amount every year, so the situation can be modeled using simple linear equations. The goal is to determine the year when the price of commodity X exceeds the price of commodity Y by Rs 60.

Given Data / Assumptions:
- In the base year 2002, price of commodity X = Rs 320.
- In 2002, price of commodity Y = Rs 740.
- Every year, the price of X increases by Rs 60.
- Every year, the price of Y increases by Rs 20.
- We assume the annual increases remain constant over the years.
- We must find the calendar year when X is exactly Rs 60 more expensive than Y.

Concept / Approach:
Because both prices increase linearly with time, we can represent them with linear expressions in terms of t, the number of years after 2002. Then we set up an equation that expresses the required condition: price of X = price of Y + 60. Solving this equation for t gives the number of years after 2002, from which we can find the actual year.

Step-by-Step Solution:
Step 1: Let t be the number of years after 2002. Step 2: Write the price of commodity X after t years: X(t) = 320 + 60 * t. Step 3: Write the price of commodity Y after t years: Y(t) = 740 + 20 * t. Step 4: We want X(t) to be Rs 60 more than Y(t), so set up the equation: 320 + 60 * t = 740 + 20 * t + 60. Step 5: Simplify the right side: 740 + 20 * t + 60 = 800 + 20 * t. Step 6: The equation is now 320 + 60 * t = 800 + 20 * t. Step 7: Bring all terms involving t to one side: 60 * t - 20 * t = 800 - 320. Step 8: This gives 40 * t = 480. Step 9: Solve for t: t = 480 / 40 = 12. Step 10: The required year is 2002 + 12 = 2014.

Verification / Alternative Check:
Check the prices in 2014: t = 12. Then X(12) = 320 + 60 * 12 = 320 + 720 = Rs 1040. Y(12) = 740 + 20 * 12 = 740 + 240 = Rs 980. The difference is 1040 - 980 = Rs 60, which matches the requirement. Checking any earlier year gives a smaller difference, so 2014 is indeed the first year when X is Rs 60 more expensive than Y.

Why Other Options Are Wrong:
Option A (2011), Option C (2012) and Option D (2017) do not satisfy the difference of exactly Rs 60 when calculated with the given annual increments. They either give a smaller or larger price gap between X and Y.

Common Pitfalls:
Students sometimes mix up the direction of the difference, setting X(t) + 60 = Y(t) instead of X(t) = Y(t) + 60, or they plug in options without forming the equation. Another common mistake is forgetting to check the year relative to the base year, leading to incorrect addition or subtraction of t from 2002.

Final Answer:
Commodity X will cost Rs 60 more than commodity Y in the year 2014.