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Varsha lives alone and dislikes cooking, so she goes out for dinner every evening. She has two favourite restaurants, $\text{Dosa Paradise}$ and $\text{Kababs Unlimited}$, to which she travels by local train. The train to $\text{Dosa Paradise}$ runs every $10$ minutes, at $0, 10, 20, 30, 40$ and $50$ minutes past the hour. The train to $\text{Kababs Unlimited}$ runs every $20$ minutes, at $8, 28$ and $48$ minutes past the hour. She reaches the station at a random time between $7:15$ pm and $8:15$ pm and chooses between the two restaurants based on the next available train/ What is the probability that she ends up eating in $\text{Kababs Unlimited}$?

  1. $\frac{1}{5}$
  2. $\frac{1}{3}$
  3. $\frac{2}{5}$
  4. $\frac{1}{2}$
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Train timings for Dosa Paradise-->

7:20

7:30

7:40

7:50

8:00

8:10

 

Train timings for Kabab Unlimited.

7:28

7:48

8:08

 

Favourable time slots-->

7:20-7:27  => 8 minutes

7:40-7:47 => 8 minutes

8:00-8:07 => 8 minutes.

 

Probability=> 24/60 => 2/5
Answer:

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