2 tables and 3 chairs together cost ₹12000. When the cost of a table is decreased by 10% and that of a chair is increased by 20%, then 3 tables and 4 chairs together cost ₹17100. What is the total original cost of 1 table and 2 chairs?

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  1. ₹6800
  2. ₹6600
  3. ₹6500
  4. ₹6300

Answer (Detailed Solution Below)

Option 2 : ₹6600
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Detailed Solution

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Given:

2 tables and 3 chairs together cost ₹12000.

Calculation:

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

2T + 3C = 12000

New cost of table = T - 0.1T = 0.9T

New cost of chair = C + 0.2C = 1.2C

New equation:

3(0.9T) + 4(1.2C) = 17100

⇒ 2.7T + 4.8C = 17100

Original equation:

⇒ 2T + 3C = 12000

Multiply original equation by 1.6:

⇒ 3.2T + 4.8C = 19200

Subtract new equation from the above equation:

⇒ 3.2T + 4.8C - (2.7T + 4.8C) = 19200 - 17100

⇒ 0.5T = 2100

⇒ T = 2100 / 0.5

⇒ T = 4200

Substitute T in original equation:

⇒ 2(4200) + 3C = 12000

⇒ 8400 + 3C = 12000

⇒ 3C = 3600

⇒ C = 1200

Total original cost of 1 table and 2 chairs:

⇒ 1T + 2C

⇒ 4200 + 2(1200) = 4200 + 2400

⇒ 6600

The total original cost of 1 table and 2 chairs is ₹6600.

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