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Question
If (3x – 4y) : (2x – 3y) = (5x – 6y) : (4x – 5y), find x : y.
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Solution
(3x – 4y) : (2x – 3y) = (5x – 6y) : (4x – 5y)
`(3x - 4y)/(2x - 3y) = (5x - 6y)/(4x - 5y)`
Applying componendo and dividendo,
`(3x -4y + 2x - 3y)/(3x - 4y - 2x + 3y) = (5x - 6y + 4x - 5y)/(5x -6y - 4x + 5y)`
`(5x - 7y)/(x - y) = (9x - 11y)/(x - y)`
5x – 7y = 9x – 11y
11y – 7y = 9x – 5x
4y = 4x
`x/y = 1/1`
x : y = 1 : 1
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