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In covering a distance of 30km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is: A. 5 kmph B. 7 kmph C. 6.25 kmph D. 7.5 kmph

In covering a distance of 30km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is:
A. 5 kmph
B. 7 kmph
C. 6.25 kmph
D. 7.5 kmph

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
Assume time taken by Sameer to cover 30km be “t”. Calculate speed of Sameer and Abhay by using the formula, Speed = Distance travelledtime taken...........(1) Complete step-by-step solution - Let the time taken by Sameer to cover a distance of 30km be “t” hours. Hence, Speed of Sameer = Distance travelledtime taken∴ Speed of Sameer = (30t)km/hour According to the question, Abhay takes 2 hours more than Sameer. Hence, the time taken by Abhay to cover a distance of 30km = (t +2) hours. Hence, Speed of Abhay = Distance travelledtime taken∴ Speed of Abhay = (30t+2)km/hour.........(2) Now, when Abhay doubles his speed, then he would take 1 hour less than Sameer. New speed of Abhay = 2× previous speed of Abhay =2× (30t+2)km/hour.........(3) Total time taken by Abhay to cover 30km with new speed, =Distance travelledNew speed of Abhay= 30(t+2)2×30 (using equation (3))=t+22hours Given that, this time taken by Abhay is equal to 1 hour less than time taken by Sameer. ⇒(t+22)=(t−1) since, time taken by sameer is equal to ''t'' hours ⇒t+2=2(t−1) ⇒t+2=2t−2 ⇒2+2=2t−t ⇒4=t ∴ “t” is equal to 4 hours. From equation (1), speed of Abhay =30t+2km/hr Putting the values of t = 4 hours, we get speed of Abhay, =(304+2)km/hr=306=5km/hr Note: You can do this question quickly by assuming Abhay speed be x and framing equation according to the question in one variable as, Let Abhay’s speed be x km/hour. Then, according to question, ⇒30x−302x=(2+1)hours⇒30x−302x=3⇒60−302x=3⇒302x=3⇒30=6x∴x=5km/hour

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