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

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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.