A car travels from Somgarh to Raipur in 35 minutes at an average speed of 69 km/h. If the average speed is increased by 36 km/h (keeping the same route and distance), how much time will the car take to cover the same distance?

Introduction: This problem tests the distance–speed–time relationship and how changing speed alters journey time for a fixed distance. By converting minutes to hours and applying D = v * t twice, we can compare the two times and compute the new time directly.

Given Data / Assumptions:

• Initial average speed v1 = 69 km/h.
• Initial time t1 = 35 minutes = 35/60 hours.
• New average speed v2 = 69 + 36 = 105 km/h.
• Distance remains the same on both trips.

Concept / Approach: For a fixed distance D, D = v1 * t1 = v2 * t2. Hence t2 = (v1 / v2) * t1. Convert t1 into hours, compute t2, then express the result in minutes for clarity.

Step-by-Step Solution:

Verification / Alternative check: Direct ratio method: time is inversely proportional to speed for fixed distance. New time = old time * (69/105) = 35 * (69/105) = 23, confirming the calculation.

Why Other Options Are Wrong: 24, 26, 27, and 29 minutes do not match the exact inverse-speed scaling from 69 km/h to 105 km/h with a 35-minute baseline.

Common Pitfalls: Forgetting to convert minutes to hours, or subtracting speeds instead of using the time ratio. Always use t2 = (v1/v2) * t1 when distance is constant.

Final Answer: 23 min