★ Given:-

▪︎COST of 23 spoons and 17 forks = ₹1770

▪︎Cost of 17 spoons and 23 forks = ₹1830

════◄••❀••►════

★ To Find:-

▪︎Cost of a spoon

▪︎Cost of a fork

════◄••❀••►════

★ Solution:-

Let the cost of a spoon be x

Let the cost of a fork be y

According to given CONDITIONS;

➥ 23x + 17y = ₹1770 ------- eq.1

➥ 17x + 23y = ₹1830 ------- eq.2

By adding eq.1 and eq.2, we get:-

23x + 17y + 17x + 23y = 1770 + 1830

➟ 23x + 23y + 17x + 17y = 3600

➟ 23(x + y) + 17(x + y) = 3600

➟ (23 + 17) (x + y) = 3600

➟ x + y = 3600 ÷ 40

➟ x + y = 90 ------- eq.3

By subtracting eq. 2 fron eq. 1,we get:-

23x + 17y - (17x + 23y) = 1770 - 1830

➟ 23x - 23y - 17x + 17y = -60

➟ 23(x - y) - 17(x - y) = -60

➟ (23 - 17) (x - y) = -60

➟ x - y = -60 ÷ 6

➟ x - y = -10 ------- eq.4

By adding eq.3 and eq.4, we get:-

x + y + (x - y) = 90 + (-10)

➟ x + x + y - y = 90 - 10

➟ 2x = 80

➟ x = 80 ÷ 2

➟ x = 40

Putting x = 40 in eq.3 we get;-

x + y = 90

➟40 + y = 90

➟ y = 90 - 40

➟ y = 50

Hence,

x = 40

y = 50

════◄••❀••►════

★ Answer:-

▪︎Cost of a spoon = ₹40

▪︎Cost of a fork = ₹50

════◄••❀••►════