The ratio of the walking speeds of A and B is 3 : 5. If B takes 18 minutes to cover a certain distance, how much time will A take to cover the same distance?

Correct option is D

Given:

- Speed ratio (A : B) = 3 : 5

- Time is inversely proportional to speed for same distance

- Time ratio (A : B) = 5 : 3

- Time taken by B = 18 minutes

Formula Used:

​$$- Speed ∝\frac{ 1 }{Time \ (for\ same\ distance)}\\\ \\- \frac{Time_A }{ Time_B} = \frac{Speed_B }{Speed_A}$$​​

Solution:

Time ratio (A : B) = 5 : 3

Let time taken by A be x minutes

Then, $$\frac{x }{ 18} = \frac{5 }{ 3 }=> x = \frac{(5 × 18) }{3} = \frac{90 }{3} = 30$$​​

Final Answer: A will take 30 minutes 
Alternate Solution: 

Ratio of speeds of A and B = 3 : 5

=> Ratio of time of A and B = 5 : 3

Let time taken by A and B be 5x and 3x respectively.

Time taken by B  = 18 
3x= 18
x = 6
Time Taken by A = 5x = 30 min 

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