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A cat leaps 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 speed of the cat to that of the dog?
- a)11 : 15
- b)15 : 11
- c)16 : 15
- d)15 : 16
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog...
15 : 16
Given :
3 dog = 4 cat;
Or, dog/cat = 4/3;
Let cat’s 1 leap = 3
meter and dogs 1 leap = 4 meter.
Then, ratio of speed of cat and dog
= 3 × 5/4 × 4= 15 : 16.
Given :
3 dog = 4 cat;
Or, dog/cat = 4/3;
Let cat’s 1 leap = 3
meter and dogs 1 leap = 4 meter.
Then, ratio of speed of cat and dog
= 3 × 5/4 × 4= 15 : 16.
Most Upvoted Answer
A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog...
Ratio of Leaps
Let's start by determining the ratio of the number of leaps made by the cat to the number of leaps made by the dog.
Given:
- The cat leaps 5 times for every 4 leaps of the dog.
This means that for every 4 leaps of the dog, the cat makes 5 leaps.
Let's assume that the dog takes 4 leaps. Then, the cat will take 5 leaps.
Ratio of Leaps = 5 : 4
Ratio of Distance Covered
Now, let's consider the ratio of the distance covered by the cat to the distance covered by the dog.
Given:
- 3 leaps of the dog are equal to 4 leaps of the cat.
This means that the distance covered by the dog in 3 leaps is equal to the distance covered by the cat in 4 leaps.
Let's assume that the distance covered by the cat in 4 leaps is d. Then, the distance covered by the dog in 3 leaps will also be d.
Ratio of Distance Covered = d : d
Ratio of Speed
Since the distance covered by the cat and the dog is the same, we can conclude that their speed is inversely proportional to the number of leaps they take.
Let's find the ratio of the speed of the cat to that of the dog.
Ratio of Speed = Leap Ratio : Distance Ratio
= 5 : 4 : d : d
= 5d : 4d
Simplifying the ratio by dividing both terms by d:
Ratio of Speed = 5 : 4
Therefore, the ratio of the speed of the cat to that of the dog is 5 : 4, which is equivalent to 15 : 16.
Hence, the correct answer is option D) 15 : 16.
Let's start by determining the ratio of the number of leaps made by the cat to the number of leaps made by the dog.
Given:
- The cat leaps 5 times for every 4 leaps of the dog.
This means that for every 4 leaps of the dog, the cat makes 5 leaps.
Let's assume that the dog takes 4 leaps. Then, the cat will take 5 leaps.
Ratio of Leaps = 5 : 4
Ratio of Distance Covered
Now, let's consider the ratio of the distance covered by the cat to the distance covered by the dog.
Given:
- 3 leaps of the dog are equal to 4 leaps of the cat.
This means that the distance covered by the dog in 3 leaps is equal to the distance covered by the cat in 4 leaps.
Let's assume that the distance covered by the cat in 4 leaps is d. Then, the distance covered by the dog in 3 leaps will also be d.
Ratio of Distance Covered = d : d
Ratio of Speed
Since the distance covered by the cat and the dog is the same, we can conclude that their speed is inversely proportional to the number of leaps they take.
Let's find the ratio of the speed of the cat to that of the dog.
Ratio of Speed = Leap Ratio : Distance Ratio
= 5 : 4 : d : d
= 5d : 4d
Simplifying the ratio by dividing both terms by d:
Ratio of Speed = 5 : 4
Therefore, the ratio of the speed of the cat to that of the dog is 5 : 4, which is equivalent to 15 : 16.
Hence, the correct answer is option D) 15 : 16.
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A cat leaps 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 speed of the cat to that of the dog?a)11 : 15b)15 : 11c)16 : 15d)15 : 16Correct answer is option 'D'. Can you explain this answer?
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