Aryan Bimal and Karan start from the same place and travel in the same direction at speeds of 15 30 ...........

Quantitative Aptitude ( CCS) Time & distance

Aryan, Bimal and Karan start from the same place and travel in the same direction at speeds of 15, 30 and 60 km per hour respectively. Bimal starts two hours after Aryan. If Bimal and Karan overtake Aryan at the same instant, how many hours after Aryan did Karan start?

4 hrs

2 hrs

3 hrs

6 hrs

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Explanation:

Let us assume that Aryan started running at 10 AM and Bimal started at 12 noon.
So, in these two hours distance travelled by Aryan is 30 km and the relative speed of Bimal with respect to Aryan is 15 km/hr.
So Bimal will overtake Aryan after =30/15 =2 hrs
So, Bimal reaches there at 2 PM.
So, Karan also overtakes Aryan at 2 PM.
Let us assume Karan takes t time to overtake Aryan and the relative speed of Karan with respect to Aryan is 45 km/hr and Aryan ran for 4 hrs.
So, distance travelled by Aryan is:
= time × speed
= 4 × 45 ……. (i)
While Karan's distance travelled is:
= t × 60 -------- (ii)
Since distance travelled by them is equal,
⇒ (i) = (ii)
⇒ 4 × 45 = t × 60
T = 3 hours
So, after 3 hrs, Karan will start running.