Question

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 1

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.