Question

A dog takes 4 leaps for every 7 leaps of a cat, but 4 leaps of a dog are equal to the 6 leaps of the cat. The ratio of speeds of dog and cat is:

• A. 16:15
• B. 5:7
• C. 6:7
• D. 8:5

Hint:

When comparing speeds, use the ratio of the distances covered in the same time period. Simplify the terms wherever possible.

Answer 1

The Correct Option is C

Let the length of one leap of the dog be \( L_d \) and the length of one leap of the cat be \( L_c \). We are given the following information: - For every 7 leaps of the cat, the dog takes 4 leaps, so the total distance covered by the dog and cat is in the ratio \( 4L_d \) to \( 7L_c \). - 4 leaps of the dog are equal to 6 leaps of the cat, so: \[ 4L_d = 6L_c \quad \Rightarrow \quad L_d = \frac{3}{2}L_c \] Now, we use this to find the ratio of their speeds. Speed is given by: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Since both animals take the same time to make their respective leaps, the ratio of speeds is simply the ratio of distances covered in the same time. The ratio of the distances covered is: \[ \frac{4L_d}{7L_c} = \frac{4 \times \frac{3}{2} L_c}{7L_c} = \frac{6L_c}{7L_c} = \frac{6}{7} \] Thus, the ratio of speeds is \( 6:7 \).