Tilak rides his cycle from his home to a certain place at a speed of 22 km/h and returns along the same route at a speed of 20 km/h. The time taken for the return journey is 36 minutes more than the time taken for the onward journey. What is the total distance traveled by Tilak (going and coming back), in kilometers?

Introduction / Context:
This question deals with a two way journey where the distances are equal but the speeds are different in each direction. The problem is designed to test a student's understanding of how changing speed affects travel time and how to work backwards from a time difference to find the actual distance. It is a common pattern in aptitude exams involving time, speed, and distance.

Given Data / Assumptions:

• Speed from home to the place (onward journey) = 22 km/h.
• Speed on the return journey = 20 km/h.
• Time for return journey is 36 minutes more than time for onward journey.
• 36 minutes = 36 / 60 hours = 0.6 hours.
• The path is the same in both directions, so the one way distance is the same.
• We must find the total distance traveled, which is twice the one way distance.

Concept / Approach:
Let the one way distance be D km. Then, the time taken for the onward journey is D / 22 hours and the time for the return journey is D / 20 hours. The difference between these two times is given as 0.6 hours. We can set up an equation for the difference in times and solve for D. The total distance traveled is 2D = D going plus D coming back.

Step-by-Step Solution:
Let D be the one way distance in km. Time onward = D / 22 hours. Time return = D / 20 hours. Time difference = D / 20 - D / 22 = 0.6 hours. Factor D: D * (1 / 20 - 1 / 22) = 0.6. Compute 1 / 20 - 1 / 22 = (22 - 20) / (20 * 22) = 2 / 440 = 1 / 220. So D * (1 / 220) = 0.6, hence D = 0.6 * 220 = 132 km. Total distance traveled = 2 * D = 2 * 132 = 264 km.

Verification / Alternative check:
Using D = 132 km, time onward = 132 / 22 = 6 hours, and time return = 132 / 20 = 6.6 hours. The difference is 0.6 hours, which is 36 minutes. This matches the problem statement perfectly and confirms that the distances and times are consistent.

Why Other Options Are Wrong:
132 km is the one way distance, not the total distance, so option 132 km corresponds to half of the journey only. Values such as 134 km, 236 km, and 200 km do not satisfy the given 36 minute time difference when substituted into the time expressions. Only 264 km correctly corresponds to twice the one way distance of 132 km and respects the given condition.

Common Pitfalls:
Students sometimes treat 132 km as the final answer by forgetting that the question asks for the total distance. Another mistake is to incorrectly compute the difference of reciprocals of the speeds. Carefully setting up the equation for the time difference and then remembering to double the one way distance helps avoid these errors.

Final Answer:
The total distance traveled by Tilak (going and coming back) is 264 km.