CAT 2023 Slot 1 · Quant · Question 8

If the average speed over the 8-hour trip is s, the distance covered is 8s km.

So the earlier odometer reading was x=26862-8s, and this must also be a palindrome.

A larger s is better, so test the options from the top.

At s=110: x=26862-880=25982, which reversed is 28952 — not a palindrome.

At s=100: x=26862-800=26062, which reversed is 26062 — a palindrome.

Since 110 fails and 100 works, and 90 and 80 are smaller, the greatest workable average speed among the options is 100 km/h.

The cap of 110 km/h on instantaneous speed is also respected, since an average of 100 is achievable without ever exceeding 110.

The answer is 100 km/h, the second option.

Shortcut. Since x and 26862 share the leading digits 2 and 6, the trip distance is at most a few hundred kilometres — so the palindrome must be of the form 26\_62. The only candidate below 26862 with the right gap is 26062, a difference of 800 km, giving \frac{800}{8}=100 km/h straight away.