Since the car travels for 1/6 of an hour at each speed i.e first 10 mins at 30 miles per hour, then for 10 mins at 25 miles per hour and so on.
Total distance it travels is 1/6(30+25+20+15+10+5) which gives us quantity A.

Since the car travels the same amount of time at each speed i.e 10 mins at each speed 30,25 ,20 so on, we can sum the speeds and divide by 6. That is simply the average of all the speeds.

Quantity B is so (30+25+20+16+10+5) /6

we can see that A and B give us the same number so the answer is C.

I could not understand how you computed the quantity A sir!

Can someone pls explain this question?

pranab223 has explained it in simple words.

If the total distance covered in 1 hour is \(D\)
then, the average speed = \(\frac{total distance covered}{total time taken} = \frac{D}{1} = D\)

Or you can solve for exact values;

Distance travelled in First 10 minutes = \(30(\frac{10}{60}) = 5\) miles

Distance travelled in next 10 minutes = \((25)(\frac{10}{60}) = 4.16\) miles

Distance travelled in next 10 minutes = \((20)(\frac{10}{60}) = 3.33\) miles

Distance travelled in next 10 minutes = \((15)(\frac{10}{60}) = 2.50\) miles

Distance travelled in next 10 minutes = \((10)(\frac{10}{60}) = 1.66\) miles

Distance travelled in Last 10 minutes = \((5)(\frac{10}{60}) = 0.83\) miles

Total distance travelled = 17.48 miles
Average speed \(= \frac{total distance covered}{total time taken} = \frac{17.48}{1}\) = 17.48 miles

Col. A: 17.48
Col. b: 17.48

Hence, option C

Even though the Karun answer is the most understandable, you have to save time in the real gre like Pranab does in his solution.