Profit and Loss – Solving a two-variable price system: If two mixers and one TV cost Rs 7000, while two TVs and one mixer cost Rs 9800, find the price of one TV set.

Introduction / Context:We are given a pair of linear equations in two variables representing item prices. Solve for the TV price.

Given Data / Assumptions:

• Let mixer price = m
• Let TV price = t
• 2m + t = 7000
• m + 2t = 9800

Concept / Approach:Use substitution or elimination to solve simultaneous linear equations.

Step-by-Step Solution:From 2m + t = 7000 ⇒ t = 7000 - 2mSubstitute in m + 2t = 9800 ⇒ m + 2(7000 - 2m) = 9800m + 14000 - 4m = 9800 ⇒ -3m = -4200 ⇒ m = 1400Then t = 7000 - 2 * 1400 = 4200

Verification / Alternative check:Check second equation: 1400 + 2 * 4200 = 9800, correct.

Why Other Options Are Wrong:2100, 2800, 3500, 3900 do not satisfy both equations simultaneously.

Common Pitfalls:Arithmetic slips when substituting or eliminating variables.

Final Answer:Rs 4200