# A bike rider is travelling at 120 km/h. After every 36 minutes, he red

A. 504 minutes

B. 360 minutes

C. 396 minutes

D. 432 minutes

### Right Answer is: C

#### SOLUTION

Let the bike rider takes n intervals of 36 min.

Distance in first 36 minutes = = 72 km.

Distance in second 36 minutes = = 66 km.

Distance in third 36 minutes = = 60 km.

and so on.

It’s an A.P., where a = 72, d = -6 and sum of first ‘n’ terms of the A.P. is 462

Now S = [2a + (n – 1)d]

462 = [144 + (n – 1)(-6)]

462 = (150 – 6n)

462 = n(75 – 3n)

3n^{2} – 75n + 462 = 0

3n^{2} – 33n – 42n + 462 = 0

3n(n – 11) – 42(n – 11) = 0

(n – 11)(3n – 42) = 0

So n = 11 or n = 14

n = 14 is not possible because at last the speed (120 – 13×10) = -10) will be negative, which is not possible.

So, the required time is = = 396 minutes.