A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps problem A cat chases a rat. For every  $5$ leaps of the rat , the cat takes $3$ leaps, but the  $2$ leaps of the cat are the same as $3$ leaps of the rat. Compare the speeds of the cat and the rat

a)$4:5$

b)$12:13$

c)$16:15$

d)none of these

solution  

clearly the  $2$ leaps of the cat are the same as $3$ leaps of the rat

so let distance of rat leap be $x$

then distance of cat's leap =$ \frac {3x}{2} $

then speed ratio = $ \frac {4.5x}{5x} $ 

$ \frac {9}{10} $ 

Am I right $?$
I see no fault in your answer.
Quicker an simple 
Assume 2 leaps of cat = 3 leaps of rat=6meter(lcm of 2;3)
NowNow 3 leap of cat is 9 m
Rat 5 leap is 10 meter
Ratio = distance /time
Time is same
So ratio 9/10