| The ratio between the rates of travelling of A and B is 2: 3 and therefore A takes 20 min more than time taken by B to reach a destination. If A had walked at double the speed, how long would he have taken to cover the distance? |
A) 30 min
B) 35 min
C) 20 min
D) 45 min
E) None of these
Correct Answer: A
Solution :
| We know that, speed is inversely proportional to time. Therefore, |
| Time taken by A: Time taken by \[B=\frac{1}{2}:\frac{1}{3}\] |
| Let B takes x min. Then, A takes \[(x+20)\min .\] |
| \[\therefore \] \[(x+20):x=\frac{1}{2}:\frac{1}{3}=3:2\] |
| \[\Rightarrow \]\[\frac{x+20}{x}=\frac{3}{2}\]\[\Rightarrow \]\[2x+40=3x\] |
| \[\therefore \] \[x=40\] |
| \[\therefore \]A takes \[(x+20)\]or \[(40+20)=60\min \] |
| \[\therefore \]At double the speed, A would have covered it in 30 min. |
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