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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 60787 Points
2 years 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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