Question
Download Solution PDF2 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Dec 9, 2024
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