Question

The cost of a table and a chair together is Rs1620. If the table costs 16% more than the chair, find the cost of each.

Answer 1

Hint – In this question assume the cost of 1 table and 1 chair to be a variable. Using constraints of the questions formulate two linear equations in two variables, to get the relation between the two variables assumed. Solve them to get the answer.
Complete step-by-step answer:
Given data
Cost of table and chair together is Rs. 1620.
Let the cost of the table be Rs x.
And the cost of the chair is Rs y.
Therefore, x + y =1620........................... (1)
Now it is given that the cost of the table is 16% more than the chair.
So construct the linear equation according to this information we have,
Therefore, x = y + 16%y
$ \Rightarrow x = y + \dfrac{{16}}{{100}}y = \dfrac{{29}}{{25}}y$
Now substitute this value in equation (1) we have,
$ \Rightarrow \dfrac{{29}}{{25}}y + y = 1620$
Now simplify this equation we have,
$ \Rightarrow \left( {29 + 25} \right)y = 1620 \times 25$
$ \Rightarrow y = \dfrac{{1620 \times 25}}{{54}} = 750$
Now from equation (1) we have,
$ \Rightarrow x + 750 = 1620$
$ \Rightarrow x = 1620 - 750 = 870$
So the cost of table and chair is Rs 870 and 750 respectively.
So this is the required answer.

Note – After taking the cost of 1 chair as y and table as x. we have formed equation x + y=1620 as the total cost is given. Key point here is we have equated the same quantity that is price in both the left hand and right hand side. Even in the formulation of the other equation x = y + 16%y, it’s the price that is being equated. Solving such types of problems need this simple approach of equating same quantities while making up of equations.