The speed of a vehicle increases by 5 km after every one hour. If the distance travelled in the first one hour was 30 km, then what was the total distance travelled in 10 hours?

Given:

The speed of a vehicle increases by 5 km every hour

The distance traveled in the first hour = 30 km

Formula used:

The sum of n numbers in Arithmetic progression = \(\frac{n}{2} [ 2a + (n-1)d ]\)

where, n = number of terms; a = first term; d = difference

Calculation:

The speed increased by 5 km for every hour,

30 km, 35 km, 40 km ...

Hence the speed for 10 hours is in Arithmetic progression with a difference of 5 km

Since the speed is given for an hour it will also be equal to the distance traveled for that hour

The sum of distance for 10 hours = \(\frac{n}{2} [ 2a + (n-1)d ]\)

⇒ \(\frac{10}{2}\) [2 × 30 + (10 - 1)5] = 5[60 + 9 × 5]

⇒ 5 (60 + 45) = 5 × 105 = 525 km.

∴ The correct answer is 525 km.