Question

23 spoons and 17 forks cost Rs.1770, while 17 spoons and 23 forks cost Rs.1830. Find the cost of each 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.