This is the basic and conceptual question from linear equations in two variables in which we have to find the cost of a spoon and a fork by solving the equations if 23 spoon and 17 forks together cost is ₹1770, while 17 spoons and 23 forks together cost ₹1830.

RS Aggarwal, Class 10, chapter 3E, question no 2

Let the cost of a spoon be Rs.x and that of a fork be Rs.y.

Then

23x + 17y = 1770 ……….(i)

17x + 23y = 1830 ………(ii)

Adding (i) and (ii), we get

40x + 40y = 3600

⇒ x + y = 90 ………..(iii)

Now, subtracting (ii) from (i), we get

6x – 6y = -60

⇒ x – y = -10 ………..(iv)

Adding (iii) and (iv), we get

2x = 80

⇒ x = 40

Substituting x = 40 in (iii), we get

40 + y = 90

⇒ y = 50

Hence, the cost of a spoon that of a fork is Rs.40 and Rs.50 respectively