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If `(10 x + 3y) : (5x + 2y) = 9 : 5`, then show that `(2x + y) : (x + 2y) = 11 : 13`.

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`(10 x + 3y) : (5x + 2y) = 9 : 5`
or , `(10x + 3y)/(5x + 2y) = 9/5`
or, `50x + 15y = 45x + 18y`
or, `50x - 45x = 18y -15y`
or, `5x = 3y " or, " x/y = 3/5`
or, `x/y = (3k)/(5k) [k ne 0]`
` :. ` let x = 3k and y = 5k.
Now, ` (2x + y) : (x + 2y) = (2x + y)/(x + 2y)`
` = (2 xx 3k + 5k)/(3k + 2 xx 5k)`
` = (6k + 5k)/(3k+10k) = (11k)/(13k) = 11/13`.
Hence `(2x + y) : (x +2y) = 11 : 13`.

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