Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 kms till then, this number again being palindromic. If Brishti never drove at more than 110 kmph, then the greatest possible average speed at which she drove during the rip, in kmph was?
Explanation:
Total distance travelled at the end of the trip = 26,862. This includes the distance which car had travelled before the trip and the distance it travels in the 8 hours of the trip.
To maximize speed in 8 hours, we need to maximize distance travelled in 8 hours. ∴ We need to minimize the distance travelled by car before the trip starts, hence we need to minimize x.
Since Brishti drove at less than 110 kmph, hence she must have travelled less than 110 × 8 = 880 kms in the last 8 hours.
∴ She must have travelled more than 26862 – 880 = 25,982 kms before the last 8 hours. ⇒ x > 25,982 and it has to be a palindrome.
Least palindrome greater than 25,982 is 26062.
∴ Car travelled at least 26062 kms before the trip, hence maximum distance travelled during the trip = 26862 – 26062 = 800 kms.
⇒ Maximum average speed for the trip = 800/8 = 100 kmph.
Hence, option (d).
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