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A car starts running with the initial speed of 40 km/h with its speed increasing every hour by 5 km/h. How many hours will it taken to cover a distance of 385 km ?
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- 81/2 h
- 91/2 h
- 9 h
- 7 h
Correct Option: D
Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
Given, sum of the series is 385
∴ a = 40, d=5, s = 385 and n= ?
Using S = n/2[2a + (n - 1)d]
⇒ 385 = n/2[80 + 5n - 5]
⇒ 770 = 5n2 + 75n
⇒ n2 + 15n - 154 = 0
⇒ n2 + 22n - 7n - 154 = 0
⇒ n(n + 22) - 7(n + 22) = 0
⇒ (n + 22) (n - 7) = 0
∴ n = 7
Remaining part = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 i.e., 1/30 th part is filled by B in 1 min
Hence, required time to fill the whole tank = (165 + 1 + 1) min = 167 min
