Solving two-item linear price equations The cost of 2 T.V. sets and 1 radio is Rs 7000, while the cost of 2 radios and 1 T.V. set is Rs 4250. Find the cost of one T.V. set.

Introduction / Context:This is a simple system of linear equations with two unknowns (prices of a T.V. set and a radio). Solving simultaneously yields the unit prices.

Given Data / Assumptions:

• 2T + R = 7000.
• T + 2R = 4250.
• Find T.

Concept / Approach:Use elimination: scale one equation to align coefficients and subtract to find one variable, then back-substitute.

Step-by-Step Solution:(1) 2T + R = 7000.(2) T + 2R = 4250.Double (2): 2T + 4R = 8500.Subtract (1): 3R = 1500 ⇒ R = 500.Substitute in (2): T + 2×500 = 4250 ⇒ T = 3250.

Verification / Alternative check:Check (1): 2×3250 + 500 = 7000 (holds). Check (2): 3250 + 2×500 = 4250 (holds).

Why Other Options Are Wrong:3000, 3160, 3240 are not solutions to the system; 'None of these' is inapplicable since 3250 is exact.

Common Pitfalls:Arithmetic slips when eliminating, or mixing the equations when substituting back.

Final Answer:Rs 3250