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?

Correct option is D

1. Understand the given information:

• Leap Ratio 1: Cat takes 5 leaps for every 4 leaps of the dog.
• Leap Ratio 2: 3 leaps of the dog are equal to 4 leaps of the cat.

2. Find a common ground:

• We need to express both leap ratios in terms of the same number of leaps for either the cat or the dog.

• Let's use Leap Ratio 2 to find the equivalent number of cat leaps for 4 dog leaps:

  • 3 dog leaps = 4 cat leaps
  • 4 dog leaps = (4/3) * 4 cat leaps = 16/3 cat leaps

3. Compare distances covered:

• In the time the cat takes 5 leaps, the dog takes 4 leaps, which is equivalent to 16/3 cat leaps.

• Distance covered by cat: 5 cat leaps

• Distance covered by dog: 16/3 cat leaps

4. Calculate the ratio of speeds:

• Speed is directly proportional to distance covered in the same time.
• Ratio of speeds (cat:dog) = Distance covered by cat : Distance covered by dog
• Ratio of speeds = 5 cat leaps : (16/3) cat leaps
• Ratio of speeds = 15 : 16

Therefore, the ratio of the speeds of the cat to that of the dog is 15:16.