Two chairs and three tables cost Rs 1025, while three chairs and two tables cost Rs 1100. Determine the absolute difference between the cost of one table and one chair.

Introduction:Linear pairs of purchases create a system of two equations in two unknowns. Often, adding or subtracting the equations directly isolates a clean expression for either the sum or difference of unit prices.

Given Data / Assumptions:

• 2C + 3T = 1025 (C = price of a chair, T = price of a table)
• 3C + 2T = 1100

Concept / Approach:Subtract the equations to eliminate one variable and isolate the difference between T and C. We are asked for |T - C|, the absolute difference.

Step-by-Step Solution:(3C + 2T) - (2C + 3T) = 1100 - 1025C - T = 75Therefore, T - C = -75, and |T - C| = 75

Verification / Alternative check:Optionally solve fully. From C - T = 75 and 2C + 3T = 1025, substitute C = T + 75 to get 2(T + 75) + 3T = 1025, so 5T + 150 = 1025, hence T = 175 and C = 250. The difference is 75, matching the result.

Why Other Options Are Wrong:

• Rs. 35 and Rs. 125: not supported by the equations.
• Cannot be determined: incorrect because we have two independent equations for two unknowns.

Common Pitfalls:

• Adding rather than subtracting, which does not isolate the difference efficiently.
• Computational slip when substituting back to check values.

Final Answer:Rs. 75