Question

23 spoons and 17 forks together cost Rs. 1770, while 17 spoons and 23 forks together cost Rs. 1830. Find the cost of a spoon and that of a fork.

Answer 1

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.