The ratio of speed of A and B is 2:3 and A takes 10 minutes more than the time taken by B to reach a destination. If A had walked at triple the
speed, and B at half the speed, the difference between time taken by A and B will be:
a) 15 minutes
b) 20 minutes
c) 25 minutes
d) 30 minutes
e) Cannot be determined
speed of A --- 2x units/min
speed of B --- 3x
time for trip for A = trip/2x = t/2x, where t is the trip
time for trip for B = trip/3x = t/3x
t/2x = t/ 3x + 10
t/(2x) - t(3x) = 10
times 6x
3t - 2t = 60x
t = 60x
case2:
speed of A = 6x
speed of B = 3x/2
time for A = t/(6x)
time for B = t/(3x/2)) = 2t/(3x)
difference in time
= 2t/(3x) - t/(6x)
= 4t/6x - t/6x = 3t/6x = t/2x
= (60x/(2x)) = 30 minutes
To solve this problem, let's break it down into smaller steps.
Step 1: Understand the given information.
- The ratio of the speed of A and B is 2:3.
- A takes 10 minutes longer than B to reach the destination.
Step 2: Set up equations to represent the given information.
Let's assume the speed of A is 2x and the speed of B is 3x (since the ratio of their speeds is 2:3).
Let's also assume that B takes t minutes to reach the destination, so A takes t + 10 minutes.
Step 3: Find the time taken by A and B in their original speeds.
To find the time taken by A, we can divide the distance by the speed:
Time taken by A = Distance / Speed = Distance / (2x)
Similarly, time taken by B = Distance / Speed = Distance / (3x)
Step 4: Set up equations for the time taken by A' and B' in their modified speeds.
Since A walks at triple the speed and B walks at half the speed, the new speeds will be 6x for A' and (3/2)x for B'.
Time taken by A' = Distance / Speed = Distance / (6x)
Time taken by B' = Distance / Speed = Distance / ((3/2)x)
Step 5: Find the difference between the time taken by A' and B'.
Difference = Time taken by A' - Time taken by B'
Difference = Distance / (6x) - Distance / ((3/2)x)
Difference = Distance * [(2/(6x)) - (2/(3x))]
Difference = Distance * [(1/(3x)) - (2/(3x))]
Difference = Distance / (3x)
From the above equation, we can see that the difference between the time taken by A' and B' is independent of the distance traveled. It only depends on the value of x, which is the ratio of the speed of A and B.
Step 6: Analyze the options.
a) 15 minutes
b) 20 minutes
c) 25 minutes
d) 30 minutes
e) Cannot be determined
Since the difference between the time taken by A' and B' is independent of the distance traveled, it is not possible to determine the exact difference without additional information. Therefore, the answer is e) Cannot be determined.