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Question
The price of 3 chairs and 2 tables is 4500 rupees and price of 5 chairs and 3 tables is 7000 rupees, then find the price of 2 chairs and 2 tables.
Solution
Let the price of 1 chair be Rs x and the price of 1 table be Rs y.
The price of 3 chairs and 2 tables is 4500 rupees
3x + 2y = 4500 ...(I)
Price of 5 chairs and 3 tables is 7000 rupees
5x + 3y = 7000 ...(II)
Multiply (I) with 3 and (II) with 2
9x + 6y = 13500 ...(III)
10x + 6y = 14000 ...(IV)
subtracting IV from III
9x + 6y = 13500
10x + 6y = 14000
− − −
−x = −500
∴ x = 500
Putting this value of x in I
3 × 500 + 2y = 4500
⇒ 1500 + 2y = 4500
⇒ 2y = 4500 - 1500 = 3000
⇒ y = 1500
Price of 2 chairs and 2 tables will be
= 2x + 2y
= 2(x + y)
= 2 (500 + 1500)
= 2 × 2000
= 4000
Thus, the price of 2 chairs and 2 tables will be Rs 4000.
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