CAT 2023 Slot 1 QA Question 8: 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 r

Question

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 r

Accepted Answer

Let the average speed during the trip be s km/h. Since the trip lasted 8 hours, the distance covered during the trip is $8s$ km.

$x = 26862 - 8s$

Since Brishti never drove at more than 110 km/h,
$8s \leq 880$
$x \geq 26862 - 880 = 25982$

To maximise s, we need the smallest palindromic odometer re