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Question
2x articles cost Rs. (5x + 54) and (x + 2) similar articles cost Rs. (10x – 4), find x.
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Solution
Cost of 2x articles = 5x + 54
Cost of 1 article = `(5x + 54)/(2x)` ….(i)
Again cost of x + 2 articles = 10x – 4
∴ Cost of 1 article = `(10x - 4)/(x + 2)` ...(ii)
From (i) and (ii),
`(5x + 54)/(2x) = (10x - 4)/(x + 2)`
⇒ (5x + 54)(x + 2) = 2x(10x - 4)
⇒ 5x2 + 10x + 54x + 108 - 20x2 - 8x
⇒ 5x2 + 10x + 54x + 108 - 20x2 + 8x = 0
⇒ -15x2 + 72x + 108 = 0
⇒ 5x2 - 24x - 36 = 0 ...(Dividing by -3)
⇒ 5x2 - 30x + 6x - 36 = 0
⇒ 5x(x - 6) + 6(x - 6) = 0
⇒ (x - 6)(5x + 6) = 0
Either x - 6 = 0,
then x = 6
or
5x + 6 = 0,
then 5x = -6
⇒ x = `(-6)/(5)`,
but it is not possible as it is in negative.
∴ x = 6.
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