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The speeds of A and B are in the ratio 2 : 3. Starting from the same position, A takes 10 minutes more than the time taken by B to reach a certain destination. If A had walked at double the speed, then he would have covered the same distance in
  • a)
    10 minutes
  • b)
    20 minutes
  • c)
    25 minutes
  • d)
    15 minutes
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The speeds of A and B are in the ratio 2 : 3. Starting from the same p...
To solve this problem, let's assume that the speeds of A and B are 2x and 3x respectively.

Let's consider the time taken by B to reach the destination as t minutes.

Speed = Distance/Time, so we can write the equation as:
2x = Distance/t

We also know that A takes 10 minutes more than B to reach the destination. So, the time taken by A would be t + 10 minutes.

Speed = Distance/Time, so we can write the equation as:
3x = Distance/(t + 10)

If A had walked at double the speed, his speed would be 4x.

Speed = Distance/Time, so we can write the equation as:
4x = Distance/t

Now, we have three equations:
2x = Distance/t
3x = Distance/(t + 10)
4x = Distance/t

Let's solve these equations to find the value of t.

To eliminate the distance, we can equate the first and third equations:
2x = 4x/t
2t = 4
t = 2 minutes

So, B takes 2 minutes to reach the destination.

Now, let's find the distance traveled by B in 2 minutes:
Distance = Speed * Time
Distance = (3x) * 2
Distance = 6x

Now, let's find the time taken by A to reach the destination:
t + 10 = 2 + 10 = 12 minutes

Now, let's substitute the values in the equation to check if A had walked at double the speed, he would have covered the same distance:
4x = Distance/12
4x = (6x)/12
4x = x/2
x = 8

So, the speed of A is 2x = 2 * 8 = 16.

Now, let's find the time taken by A to cover the distance:
Time = Distance/Speed
Time = 6x/16
Time = (6 * 8)/16
Time = 3 minutes

Since A takes 3 minutes to cover the distance when walking at double the speed, the correct option is (D) 15 minutes, as it is 10 minutes more than the time taken by B (2 minutes).
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The speeds of A and B are in the ratio 2 : 3. Starting from the same position, A takes 10 minutes more than the time taken by B to reach a certain destination. If A had walked at double the speed, then he would have covered the same distance ina)10 minutesb)20 minutesc)25 minutesd)15 minutesCorrect answer is option 'D'. Can you explain this answer?
Question Description
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