A cat takes 7 steps for every 5 steps of a dog, but 5
steps of a dog are equal to 6 steps of cat. What is the ratio of speed of
cat to that of dog?
(a) 24:25 (b) 42: 25 (c) 24:19 (d) 25:42
Answers
Given : A cat takes 7 steps for every 5 steps of a dog, but 5 steps of a dog are equal to 6 steps of cat.
To Find : What is the ratio of speed of cat to that of dog?
Solution:
A cat takes 7 steps for every 5 steps of a dog
5 steps of a dog are equal to 6 steps of cat.
A cat takes 7 steps when dog take 6 Steps of Cat
Hence Ratio of Speed of Cat : Dog = 7 : 6
None of given option is correct
Verification with Example
Let say 1 Step of dog = 6 cm => 5 step of dog = 30 cm
=> 6 step of cat = 30 cm
Then step of cat = 5 cm
A cat takes 7 steps for every 5 steps of a dog,
=> Distance by cat in 7 Steps = 7 * 5 = 35 cm
Distance by dog in 5 steps = 5 * 6 = 30 cm
Ratio of Speed of Cat : Dog = 35 : 30
=> 7 : 6
None of the given option is correct
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Answer:
the answer will be option (E) as none of the give options is correct
Step-by-step explanation:
it is given that :-
7 steps of cat = 5 steps of dog and
time taken for 6 steps of dog = time taken for 5 steps of cat
let's assume that a cat moves 1 cm in 1 step
then we can say that the dog moves 7/5 cm in 1 step
similarly,
lets assume that a dog takes 1 sec to move 1 step
then the time take by cat per step is 5/6 sec
we also know that,
Speed = distance / time
so,
the speed of dog = 7/5 cm/sec
the speed of cat = 1/(5/6) = 6/5 cm/sec
hence,
speed of cat : speed of dog = (7/5) : (6/5) = 7:6
P.S.:-
if instead of "5 steps of dog is equal to 6 steps of cat" it would have been given that "6 steps of the dog is equal to 5 steps of cat" then the ans would have been option (D) 25 : 16