Two cars start together 'm' the same direction from the same place. The first goes with uniform speed 10km/h. The second goes at a speed of 8km/h m the first hour and increases the speed by 1/2km m each succeeding hour .After how many hours will the second car overtake the first car if both cars goes non stop.

Dear Kushal
Let the second car overtakes the first car after n hours.
Hence
Distance covered by first car = distance covered by second car
10n = 8 + (8 +1/2) + (8 + 2/2) + (8+3/2) + .......+(8 + n-1/2)
10 n = 8n + 1/2 [1 +2 +3 + 4+.......(n-1)]
2n = (1/2)[n(n-1)/2]
4n = n(n-1)/2
8 n = n² - n
n² - 9n = 0
n = 9
Hence answer is 9 hours
Regards
Arun (askIITians forum expert)

Dear Student,
Please find below the solution to your problem.

Let the second car overtakes the first car after n hours.
Hence Distance covered by first car = distance covered by second car
10n = 8 + (8 +1/2) + (8 + 2/2) + (8+3/2) + .......+(8 + n-1/2)
10n = 8n + 1/2 [1 +2 +3 + 4+.......(n-1)]
2n = (1/2)[n(n-1)/2]
4n = n(n-1)/2
8 n = n² - n
n² - 9n = 0
n = 9

Thanks and Regards