If A:B = 2:3, B:C = 5:8, and C:D = 6:7, then A:D = ____?

Q.If A:B = 2:3, B:C = 5:8, and C:D = 6:7, then A:D = ____? (a) 2:7 (b) 7:2 (c) 5:8 (d) 5:14

Answer: D

\(∵ A:B=2:3\)
Or, \(\cfrac{A}{B} = \cfrac{2}{3}\)
Similarly, \(\cfrac{B}{C}=\cfrac{5}{8}\)
and \(\cfrac{C}{D}=\cfrac{6}{7}\)

\(∴ \cfrac{A}{B}×\cfrac{B}{C}×\cfrac{C}{D} = \cfrac{\cancel2}{\cancel3}×\cfrac{5}{\cancel{8}\cancel{4}2}×\cfrac{\cancel{6}\cancel2}{7}\)
Or, \(\cfrac{A}{D}=\cfrac{5}{14}\)

\(∴ A:D=5:14\) (Answer)