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प्रश्न
If `{ 3x - 5y }/ ( 5z + 3y ) = ( x + 5z )/( y - 5x ) = ( y - z )/ ( x - z )`then show that every ratio = `x/y`.
उत्तर
`( 3x - 5y )/( 5z + 3y) = ( x +5z )/( y - 5x ) = ( y - z )/( x -z )` ...[Multiplying numerator and denominator of 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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