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\(a:b = 3:4\)
বা, \(\cfrac{a}{b}=\cfrac{3}{4}\)
বা, \(a=\cfrac{3b}{4}\)

আবার, \(x:y =5:7\)
বা, \(\cfrac{x}{y}=\cfrac{5}{7}\)
বা, \(x=\cfrac{5y}{7}\)

\(\therefore (3ax-by) : (4by –7ax)\)
\(=(3\times \cfrac{3b}{4}\times \cfrac{5y}{7} -by)\) \(: (4by-7\times \cfrac{3b}{4}\times \cfrac{5y}{7})\)
\(=(\cfrac{45by}{28}-by):(4by-\cfrac{105by}{28})\)
\(=(\cfrac{45}{28}-1):(4-\cfrac{105}{28})\)
\(=(\cfrac{45-28}{28}):(\cfrac{112-105}{28})\)
\(=17:7\)