question_answer

ABC is a triangle in which \[DE||BC\] and \[AD:DB=5:4.\] Then, \[DE:BC\]is                                               [SSC (CGL) 2014]

A) 4 : 9                             

B) 5 : 9

C) 4 : 5                             

D) 9 : 5

Correct Answer: B

Solution :

\[\frac{AD}{DB}=\frac{5}{4}\]

\[\frac{AD}{AB}=\frac{5}{5+4}\]

\[[\because AB=AD+DB]\]

Then, \[\frac{AD}{AB}=\frac{5}{9}\]

Similarly, \[\frac{AD}{AB}=\frac{DE}{BC}=5:9\]