Question

Michael Schamacher is traveling in his car. In the first hour he cover 17 km and each subsequent hour he travelled 2 km less than the hour before. Calculate how much hours would it take to cover a distance of 72 km?
1. 5 hours
2. 6 hours
3. 7 hours
4. 8 hours

Answer 1

Correct Answer - Option 2 : 6 hours

Given∶

Total Distance = 72 kms

In the 1st hour he cover 17 km.

After that, each subsequent hour he travelled 2 km less than the hour before.

Formula Used∶

Sum of n terms of an A.P.

S_n = n/2[2a + (n - 1)d]

Calculation∶

Here, a = 17 and d = (15 - 17) = - 2.

Let the sum of n terms be 72. Then,

S_n = 72

⇒ n/2 {2a + (n - 1)d} = 72

⇒ n {2 × 17 + (n - 1) × (- 2)} = 144

⇒ n(36 - 2n) = 144 

⇒ 2n²- 36n + 144 = 0

⇒ n² - 18n + 72 = 0 

⇒ n² - 12n - 6n + 72 = 0

⇒n(n - 12) - 6(n - 12) = 0

⇒ (n - 12) (n - 6) = 0

⇒ n= 6 or n = 12

Here n = 12 is not possible.

∴ He takes 6 hours to cover a distance of 72 km.