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Deepak Bora
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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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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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  1. 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 – 17×50)/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

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