X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?

The correct option is D - 6.

[as per provisional answerkey]

Solution

To find how many minutes early Y completes the journey, we must calculate the total time taken by X and Y separately and then find the difference.
Formula used: Time = Distance / Speed
Note: Since speeds are in km/hr, we multiply by 60 to convert the time into minutes.

Step 1: Calculate time taken by X
1st segment: 1 km at 5 km/hr. Time = 1/5 hr = $(1/5)\times 60=12$ minutes.
2nd segment: 2 km at 10 km/hr. Time = 2/10 hr = $(1/5)\times 60=12$ minutes.
3rd segment: 3 km at 4 km/hr. Time = 3/4 hr = $(3/4)\times 60=45$ minutes.
Total time for X = 12 + 12 + 45 = 69 minutes.

Step 2: Calculate time taken by Y
1st segment: 1 km at 4 km/hr. Time = 1/4 hr = $(1/4)\times 60=15$ minutes.
2nd segment: 2 km at 10 km/hr. Time = 2/10 hr = $(1/5)\times 60=12$ minutes.
3rd segment: 3 km at 5 km/hr. Time = 3/5 hr = $(3/5)\times 60=36$ minutes.
Total time for Y = 15 + 12 + 36 = 63 minutes.

Step 3: Calculate the difference
Difference = Time taken by X - Time taken by Y
Difference = 69 minutes - 63 minutes = 6 minutes.
Therefore, Y completes the journey 6 minutes earlier than X.

Why the other options are incorrect

• Option (a) - 3: This value is incorrect; it might result from a calculation error in the third segment of Y's journey or a subtraction error.
• Option (b) - 4: This value is incorrect; it does not match the calculated difference of 6 minutes derived from the segment-wise time analysis.
• Option (c) - 5: This value is incorrect; it likely stems from rounding fractions prematurely instead of converting to minutes accurately.

Key Concept

Total time for a journey with variable speeds is the sum of the times taken for each individual segment (Time = Distance / Speed).