A policeman starts to chase a thief. When the thief goes 12 steps, the policeman moves 9 steps. 6 steps of the policeman is equal to 9 steps of the thief. The ratio of the speed of the thief to that of the policeman is:

Correct option is D

Given:

12 steps of thief = 9 steps of policeman

6 steps of policeman = 9 steps of thief

Solution:

6 steps of policeman = 9 steps of thief

1 step of policeman =$$\frac{9}{6}$$​ steps of thief

9 steps of policeman = $$9 \times \frac{9}{6}$$​ steps of thief = $$\frac{27}{2}$$​ steps of thief

The ratio of speeds of policeman and thief = Ratio of distance covered by policeman and thief in a same time

Thief moves 12 steps in same time policeman moves 9 steps

= 12 : 9 ( But we calculated 9 steps of policeman =  $$\frac{27}{2}$$​steps of thief)

= 12 : $$\frac{27}{2}$$​​

= 24 : 27

= 8 : 9