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The cost of 2 tables and 3 chairs is ₹540, while that of 2 tables and 1 chair is ₹470. What is the difference in the cost of 2 tables and 2 chairs?
₹345
₹400
₹365
₹425
₹365
Subtract the two equations: (2T + 3C) - (2T + 1C) = 540 - 470. This gives 2C = 70. The question asks for the difference in cost between '2 tables and 3 chairs' and '2 tables and 2 chairs', which is simply the cost of 1 chair. Calculating 2C = 70, so 1C = 35. The difference between (2T+3C) and (2T+2C) is 1 chair, which is 35.
Cost of 2 tables and 3 chairs = ₹540. Cost of 2 tables and 1 chair = ₹470.
2T+3C=540, 2T+1C=470
Subtract the two equations: (2T + 3C) - (2T + 1C) = 540 - 470. This gives 2C = 70. The question asks for the difference in cost between '2 tables and 3 chairs' and '2 tables and 2 chairs', which is simply the cost of 1 chair. Calculating 2C = 70, so 1C = 35. The difference between (2T+3C) and (2T+2C) is 1 chair, which is 35.
Students often solve for the cost of a table (T) and a chair (C) separately, which is unnecessary and time-consuming. The question specifically asks for the cost difference between '2 tables + 3 chairs' and '2 tables + 2 chairs', which is just the cost of one chair.
Define the equations
Let the cost of a table be T and a chair be C. We are given: (1) 2T+3C=540 and (2) 2T+1C=470.
2T+3C=540
Find the cost of one chair
Subtract equation (2) from equation (1) to eliminate T: (2T+3C)−(2T+1C)=540−470. This simplifies to 2C=70.
2C=70⟹C=35
Calculate the difference
The question asks for the difference between the cost of 2 tables and 3 chairs (540) and 2 tables and 2 chairs. The difference is (2T+3C)−(2T+2C)=C. Since C=35, the difference is ₹35.
Difference=1C=35
C is correct because the difference between 2 tables + 3 chairs and 2 tables + 2 chairs is exactly the price of one chair, which is ₹35.
This type of problem frequently appears in RRB and SSC exams. Always look for what the question asks for (the difference) instead of solving for every individual variable, as it saves significant time.
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