Ten chairs and six tables together cost ₹5,140; three chairs and two tables together cost ₹1,635. What is the cost of 1 chair and 1 table?

Question

Accepted Answer

Let the cost of one chair be C and one table be T.

From the problem, we have two equations:
1) 10C + 6T = 5140
2) 3C + 2T = 1635

Multiply the second equation by 3 to align with the first:
(3C + 2T) * 3 = 1635 * 3
=> 9C + 6T = 4905

Subtract this from the first equation:
(10C + 6T) - (9C + 6T) = 5140 - 4905
=> C = 235

Substitute C = 235 into the second equation:
3(235) + 2T = 1635
=> 705 + 2T = 1635
=> 2T = 1635 - 705 = 930
=> T = 465

Cost of 1 chair + 1 table = C + T = 235 + 465 = 700

However, the options given are ₹900, ₹600, ₹800, ₹700. The correct cost is ₹700.

Rechecking the subtraction step:
10C + 6T = 5140
9C + 6T = 4905
Subtracting:
(10C - 9C) + (6T - 6T) = 5140 - 4905
C = 235

Substitute C = 235 in 3C + 2T = 1635:
3*235 + 2T = 1635
705 + 2T = 1635
2T = 930
T = 465

Sum = 235 + 465 = 700

Therefore, the cost of one chair and one table is ₹700.

Answer

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