Profit & loss — linked prices for tables and chairs The cost of 2 tables equals the cost of 5 chairs. The difference between the price of one table and one chair is Rs 1200. Find the cost of one chair.

Introduction / Context:In profit and loss and basic algebra questions, proportional price relations are common. Here, the prices of tables and chairs are related by a ratio, and a fixed difference is also given. We must use simultaneous relations to compute the unit price of a chair.

Given Data / Assumptions:

• 2 tables cost = 5 chairs cost.
• Difference between the price of 1 table and 1 chair = Rs 1200.
• All items are identical in type and quality.

Concept / Approach:Translate the statements into algebra using unit prices: let T be the cost of one table and C be the cost of one chair. From 2T = 5C, we get T = 2.5C. Use the given difference T - C to form a second equation and solve for C.

Step-by-Step Solution:Let T = price of one table, C = price of one chair.Given: 2T = 5C ⇒ T = 2.5C.Difference: T - C = 1200.Substitute T = 2.5C: 2.5C - C = 1200 ⇒ 1.5C = 1200.Therefore, C = 1200 / 1.5 = 800.

Verification / Alternative check:If C = 800, then T = 2.5 × 800 = 2000. Difference T - C = 2000 - 800 = 1200 (matches). Also 2T = 4000 and 5C = 4000 (consistent).

Why Other Options Are Wrong:Rs 600, Rs 700, Rs 900, Rs 1,000 do not satisfy both equations simultaneously.

Common Pitfalls:Confusing the ratio 2T = 5C as T:C = 2:5 (it is actually T:C = 2.5:1). Forgetting to use the difference equation leads to underdetermination.

Final Answer:Rs 800