Question : A is twice as fast as B and B is thrice as fast as C. The journey covered by C in $1\frac{1}{2}$ hour will be covered by A in:
Option 1: 15 minutes
Option 2: 30 minutes
Option 3: 1 hour
Option 4: 10 minutes
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Correct Answer: 15 minutes
Solution :
Given: A is twice as fast as B and B is thrice as fast as C. The journey is covered by C in $1\frac{1}{2}$ hour.
Let the speed of C be $x$ metre/min.
So, the speed of B will be $3x$ metre/min.
And the speed of A will be $6x$ metre/min.
Let the time taken by A be $y$ minutes.
Here, time taken by C = $1\frac{1}{2}$ hour = $\frac{3}{2}×60 = 90$ minutes
As speed is inversely proportional to time,
The ratio of the speed of A and C = The ratio of the time taken by C and A
⇒ $6x:x=90:y$
⇒ $\frac{6}{1}=\frac{90}{y}$
⇒ $y=\frac{90}{6}=15$ minutes
Hence, the correct answer is 15 minutes.
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