An Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.

Here the cost of n folks and n spoon together is given you have to find the cost of 1 spoon and 1 folk.

This is the Question Number 2 Exercise 3E of RS Aggarwal Solution.

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# 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.

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let spoon be x and fork be y

23 spoon and 17 forks together cost rs 1770

so, 23x + 17y = 1770

23x = 1770 – 17y

x = (1770 – 17y)/23…………(1)

17 spoon and 23 forks together cost rs 1830

so, 17x + 23y = 1830…………(2)

substitute (1) in (2)

17((1770 – 17y)/23) + 23y = 1830

(30090 – 289y + 529y)/23 = 1830

30090 + 240y = 42090

240y = 42090 – 30090

240y = 12000

y = 12000/240

y = 50

substitute y in (1)

x = (1770 – 17Ã—50)/23

x = (1770 – 850)/23

x = 920/23

x = 40

so, cost of spoon is x = 40 rupees and cost of fork is y = 50