NIACL Model Paper 2 with solutions for free online practice

Question : 16 of 100

Marks: +1, -0

Two cars start together in the same direction from the same place. The first goes with a uniform speed of 10 km/h. The second goes at a speed of 8 km/h in the first hour and increases its speed by

1/2

km with each succeeding hour.
After how many hours will the second car overtake the first one, if both go non-stop?

9 horns
5 hours
7 horns
8 hours
None of these

Validate

Solution:

Let the second car overtakes the first car after t hours. Distance covered by the first car = Distance covered by the second car.
⇒

10 t=8+[8+1/2]+[8+2/2]+......+[8+{t-1}/2]

10t =8t+1/2[1+2+.....+(t-1)]

10t =8t +1/2 {t(t-1)}/2 or 2t =1/4 (t^2-t)

⇒ t=9 hrs. [ t # 0 ]

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