Multiple choice

Mohan travels a certain distance with a uniform speed. If he increases his speed by 3 km per hour, then he takes 40 minutes less. If he reduces his speed by 2 km per hour, then he takes 40 minutes more. What is the normal speed of Mohan?

  1. 8 km/hour

  2. 10 km/hour

  3. 12 km/hour

  4. 13 km/hour

  5. 15 km/hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed be v and distance be d. d/v - d/(v+3) = 40/60 = 2/3. d/(v-2) - d/v = 40/60 = 2/3. d(3/(v(v+3))) = 2/3 => d = 2v(v+3)/9. d(2/(v(v-2))) = 2/3 => d = v(v-2)/3. Equating: 2v(v+3)/9 = v(v-2)/3 => 2v+6 = 3v-6 => v = 12.

AI explanation

Let the normal speed be v km/hour and the usual time be t hours, making the distance equal to vt. Using the conditions, we set up vt / (v + 3) = t - (2/3) and vt / (v - 2) = t + (2/3), where 40 minutes is 2/3 of an hour. By cross-multiplying and rearranging both equations, we get 2v = 3t - 2 and 2t = 2v + 3. Solving this system, we substitute to find v = 12, meaning the normal speed is 12 km/hour.

Keep practicing — related questions