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If a : b = 3 : 4 " and " x : y = 4 : 5,...

If ` a : b = 3 : 4 " and " x : y = 4 : 5`, then find the value of `(3ax - by)/(5by-7ax)`

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Given that , ` a : b = 3 : 4, :. a/b = 3/4`
Again, ` x : y = 4 : 5 " or, " x/y = 4/5`
Now, Given quantity ` = (3ax-by)/(5by - 7ax) = ((3ax)/(by) - 1)/(5-(7ax)/(by)) ` [Dividing by ]
` = (3. 1/b*x/y-1)/(5 - 7 . a/b * x/y)`
` = (3xx 3/4 xx 4/5 -1)/(5 - 7 xx 3/4 xx 4/5)`
` = (9/5 -1)/(5-21/5) = ((9-5)/5)/((25-21)/5) = (4/5)/(4/5) = 1`
Hence the required value = 1.
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