A cat takes \(5\) leaps for every \(4\) leaps of a dog, but \(3\) leaps of the dog are equal to \(4\) leaps of the cat. What is the ratio of the speeds of the cat to that of the dog? একটি বিড়াল কুকুরের \(4\) লাফের সময়ে \(5\) লাফ দেয়, এবং কুকুরের \(3\) লাফ বিড়ালের \(4\) লাফের সমান। বিড়াল ও কুকুরের বেগের অনুপাত কত?

Let length of one leap of cat = \(C\)

Let length of one leap of dog = \(D\)

Given:

\[ 3D = 4C \]

\[ D = \frac{4}{3}C \]

Also,

Cat takes \(5\) leaps while dog takes \(4\) leaps in same time.

Speed of cat = \[ 5C \]

Speed of dog = \[ 4D \]

Substitute \(D = \frac{4}{3}C\):

\[ 4D = 4 \times \frac{4}{3}C = \frac{16}{3}C \]

Ratio of speeds:

\[ 5C : \frac{16}{3}C \]

\[ = 15 : 16 \]

Correct Answer: D