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If A:B=5:6, B:C=4:7 then A:C = 5:7.

since A:B=5:6

and B:C=4:7

then LCM of the value of B in both the given ratios=12

A:B=(5:6)*12

B:C=(4:7)*12

A:B=60:72

B:C=48:84

therefore A:C = 60:84

which can be simplified by dividing by 12 into 5:7