Question

The total cost of 3 tables and 2 chairs is Rs. 745. If one table costs Rs. 40 more than that of one chair, find the price of each table and chair respectively.
a. Rs. 160, Rs. 120
b. Rs. 165, Rs. 125
c. Rs. 200, Rs. 160
d. Rs. 120, Rs. 80

Answer 1

Hint: In order to solve this question, we will consider the cost of 1 table as Rs. x and the cost of 1 chair as Rs. y. Then we will form 2 linear equations of 2 variables and will apply the substitution method to get the cost of 1 table and 1 chair.

Complete step-by-step answer:
In this question, we have been asked to find the cost of 1 table and 1 chair when it is given that the total cost of 3 tables and 2 chairs is Rs. 745 and that one table costs Rs. 40 more than that of one chair. To solve this question, let us consider the cost of 1 table as Rs. x and the cost of 1 chair as Rs. y.
So, according to the question, we have been given that the total cost of 3 tables and 2 chairs is Rs. 745. So, we can write it as,
3x + 2y = 745 ……… (i)
We also have been given that the cost of one table is Rs. 40 more than the cost of one chair. So, we can write,
x = 40 + y ……… (ii)
From equation (ii), we will put the value of x in equation (i). Therefore, we get,
3 (40 + y) + 2y = 745
5y + 120 = 745
5y = 745 – 120
5y = 625
$y=\dfrac{625}{5}$
y = 125 ……… (iii)
Now, we will put the value of y in equation (ii). So, we get,
x = 40 + 125
x = 165 ……… (iv)
From equation (iii) and equation (iv), we can say that the cost of 1 table is Rs. 165 and the cost of 1 chair is Rs. 125.
Therefore, option (b) is the correct answer.

Note: While solving this question, we can apply the hit and trial method by substituting the options for the pair of linear equations, so we will obtain and get the final answer but that can be a time consuming method and the chances of calculation mistakes will also increase.