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Question
If `(3x - 5y)/(5z + 3y) = (x + 5z)/(y - 5x) = (y - z)/(x - z)`then show that every ratio = `x/y`.
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Solution
`( 3x - 5y )/( 5z + 3y) = ( x +5z )/( y - 5x ) = ( y - z )/( x -z )` ...[Multiplying numerator and denominator of the third ratio by 5]
⇒ `(3x - 5y)/(5z + 3y) = (x +5z)/(y - 5x) = [5(y - z)]/ [5(x - z)]`
= `[(3x - 5y) + x + 5z) + 5(y - z)]/[(5z +3y) + (y - 5x) + 5(x - z)]` ...( Theorem of equal ratios)
⇒ `[3x - 5y + x + 5z + 5y - 5z]/[5z +3y + y - 5x + 5x - 5z]`
⇒ `[3x - cancel(5y) + x + cancel(5z) + cancel(5y) - cancel(5z)]/[cancel(5z) +3y + y - cancel(5x) + cancel(5x) - cancel(5z) ]`
⇒ `[4x]/[ 4y]`
⇒ `x /y`
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