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# The cost of 9 chairs and 3 tables is Rs306, while the cost of 6 chairs and 3 tables is Rs246.Then the cost of 6 chairs and 1 table is$(a){\text{ Rs 161}} \\ (b){\text{ Rs 162}} \\ (c){\text{ Rs 169}} \\ (d){\text{ Rs 175}} \\$

Last updated date: 17th Mar 2023
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Hint – We are unaware of the cost of a single chair and a single table, so considering the price of a single item as a variable can help . Form two different linear equations by the conditions given in the question.

Let the price of a single chair $= {\text{ Rs x}}$
Let the price of a single table $= {\text{ Rs y}}$
Now it’s given that cost of 9 chairs and 3 tables is Rs306, thus the mathematical equation that is formed using this information is
$9x + 3y = 306$………………….. (1)
Now it is also given that cost of 6 chairs and 3 tables is Rs246, thus the mathematical equation that is formed using this information is
$6x + 3y = 246$……………….. (2)
Now subtracting equation (2) and equation (1)
$6x + 3y - 9x - 3y = 246 - 306$
On solving we get
$- 3x = - 60 \\ \Rightarrow x = 20 \\$
Now putting x in equation (1)
$9 \times 20 + 3y = 306 \\ \Rightarrow 3y = 306 - 180 \\ \Rightarrow 3y = 126 \\ \Rightarrow y = 42 \\$
Now we have the cost of one chair, x=20 and one table, y=40.
Thus now we need to find cost of 6 chairs and 1 table that is the mathematical equation that we need to evaluate is $6x + y$……………………….. (3)
Putting the values of x and y in equation (3)
$6 \times 20 + 42 = 162$
Thus the cost of 6 chairs and 1 table is Rs162
Hence option (b) is correct.

Note – Whenever we face such types of problems the key concept that we need to keep in mind is that we always try and find out the cost of a single item, by forming different linear equations by the information provided in the question. Then apply any of methods of elimination or substitution to solve the equations.