# 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}} \\

$

Answer

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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.

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.

Last updated date: 24th Sep 2023

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