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CAT 2023 Set-1 | Quantitative Aptitude | Question: 13

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Brishti went on an $8$-hour trip in a car. Before the trip, the car had travelled a total of $x \mathrm{~km}$ 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 $26862 \mathrm{~km}$ till then, this number again being palindromic. If Brishti never drove at more than $110 \mathrm{~km} / \mathrm{h}$, then the greatest possible average speed at which she drove during the trip, in $\mathrm{km} / \mathrm{h}$, was

  1. $90$
  2. $100$
  3. $80$
  4. $110$

     

1 Answer

1 1 vote
Assume distance in trip to be $dis_{trip}$.

We need to find the greatest average speed at which she drove.

$Speed_{avg} = \frac{distance}{time}$ , we are already given time of trip as $8\space hours$, so we need to maximize the distance to get the greatest average speed.

The maximum distance she could have covered during the trip would be $110\frac{km}{hr}*8hr=880\space km$. Therefore, $dis_{trip} \leq 880\space km $.

$x\geq 26862-880\space \rightarrow x\geq 25982\space km$ , we are given a condition that $x$ must be an palindrome. Nearest palindrome greater to $25982$ is $26062$.

$dis_{trip} = 26862-26062=800\space km$

$Speed_{avg} = \frac{800\space km}{8\space hour} = 100\space km/hr$

Hence option $B$ is the answer
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