Multiple choice

Raghu sets off on his bike from Asansol towards Kolkata at a certain speed, intending to reach Kolkata at 10 AM. After covering a certain distance, he realises that he would be able to cover only three-fourth of the intended distance by 10 AM. He, therefore, increases his speed by 50% and reaches Kolkata at 10 AM. What fraction of the total distance did he cover at his initial speed?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D be the total distance and T be the time remaining. He covers 3/4 D in time T. Speed v = (3/4 D) / T. He needs to cover the remaining 1/4 D in the same time T, but at speed 1.5v. 1/4 D = (1.5v) * T_remaining. This implies he covers 1/4 of the distance at the increased speed.

AI explanation

Let the total distance be D and the initial speed be S, meaning the originally planned travel time is D/S. Raghu travels some fraction of the distance at speed S, and then increases his speed by 50 percent, making his new speed 1.5S for the rest of the journey. The problem states that by travelling at the initial speed until 10 AM, he would have covered exactly three-fourths of D, leaving one-fourth of D to be covered at the increased speed; thus, the fraction of the total distance he covered at his initial speed before increasing his speed is one-fourth.

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