Let the cost of each spoon and each fork are x and y respectively.

According to question,

23 × (cost of each spoon) + 17 × (cost of each fork) = 1770, and

17 × (cost of each spoon) + 23 × (cost of each fork) = 1830

∴ 23x + 17y = 1770.....(1)

17x + 23y = 1830.....(2)

from equation (1), we get -

x = (1770 - 17y)/23.....(3)

substituting the value of x in equation (2), we get -

⇒ 30090 + 240y = 42090

⇒ 240y = 12000

∴ y = 50

substituting the value of y in equation (3), we get -

x = 40

Thus the cost of each spoon is Rs. 40 and that of a fork is Rs. 50.