Question

A car driver starts at 90 kmph and he increases his speed in every 2 hours by 3 kmph (i.e. he increases by 3 kmph at the start of 2 hours and remains constant throughout the next 2 hrs). What is the maximum distance covered by him in 24 hours?

• A. 2550 km
• B. 2556 km
• C. 2430 km
• D. 2700 km
• E. None of these

Answer 1

The correct option is B

2556 km

Speed of the rider = 90 kmph

Distance covered in 1st 2 hours = 180 km

He increased his speed in every 2 hours by 3 kmph.

Distance covered in every 2 hours will be 180, 186, 192,... upto 12 terms (for 24 hours)

The above series is an A.P series

Sum of first n terms = $\frac{n}{2}\times (2a+(n-1\left)d\right)$

Here, a = 180, d = 6 and n = 12

Sum of first 12 terms = $\frac{12}{2}$ $\times$(2(180)+(11)6) = 6(360 + 66) = 6(426) = 2556

Hence, he covers 2556 km in 24 hours