A car starts with a speed of 60 km/h with its speed increasing every o

1.	A car starts with a speed of 60 km/h with its speed increasing every one hour by 5 km/h. In how many hours will it cover 435 kms?1. 4 hrs2. 6 hrs3. 7 hrs4. 5 hrs
Answer» Correct Answer - Option 2 : 6 hrs Given: The initial speed of the car = 60 km/h Increase in speed per hour = 5 km/h Distance to be covered = 435 km Formula used: Sum of n-terms of an A.P is given by S_n = (n/2) [2a + (n - 1)d] where n = number of terms, a = 1^st term, d = common difference Calculation: Let n be the time taken by the car to cover 435 km The initial speed of the car = 60 km/h Speed for next hour = 65 km/h and so on According to the question, The distance covered by the car in 1st hour is 60km The distance covered by the car in 2nd hour is 65km and so on 60 + 65 + ............ = 435 Here S_n = 435, a = 60 and d = 65 - 60 ⇒ 5 Now, 435 = (n/2) [2 × 60 + (n - 1) × 5] ⇒ 870 = 5n [24 + n - 1] ⇒ 174 = n [23 + n] ⇒ n [n + 23] = 6 × 29 ⇒ n [n + 23] = 6 × [6 + 23] ⇒ n = 6 ∴ The time taken by the car to cover 435 km is 6 hour.

A car starts with a speed of 60 km/h with its speed increasing every one hour by 5 km/h. In how many hours will it cover 435 kms?1. 4 hrs2. 6 hrs3. 7 hrs4. 5 hrs

Answer» Correct Answer - Option 2 : 6 hrs

Given:

The initial speed of the car = 60 km/h

Increase in speed per hour = 5 km/h

Distance to be covered = 435 km

Formula used:

Sum of n-terms of an A.P is given by

S_n = (n/2) [2a + (n - 1)d]

where n = number of terms, a = 1^st term, d = common difference

Calculation:

Let n be the time taken by the car to cover 435 km

The initial speed of the car = 60 km/h

Speed for next hour = 65 km/h and so on

According to the question,

The distance covered by the car in 1st hour is 60km

The distance covered by the car in 2nd hour is 65km and so on

60 + 65 + ............ = 435

Here S_n = 435, a = 60 and

d = 65 - 60

⇒ 5

Now,

435 = (n/2) [2 × 60 + (n - 1) × 5]

⇒ 870 = 5n [24 + n - 1]

⇒ 174 = n [23 + n]

⇒ n [n + 23] = 6 × 29

⇒ n [n + 23] = 6 × [6 + 23]

⇒ n = 6

∴ The time taken by the car to cover 435 km is 6 hour.