(a)
Scenario I : Let the minimum distance between the two would be 40km after x minutes.
Since distances travelled by Devanand and Pradeep are at right angle, therefore
(50 – 3x)
‌2+ (4x)
‌2= 40
‌2⇒ 2500 + 9x
‌2 – 300x + 16x
‌2 – 1600 = 0
⇒ 25x
‌2 – 300x + 900 = 0
⇒ x = 6, which is possible.
Hence, the minimum distance between the two can be 40 km in Scenario I.
Scenario II : Since, Devanand walks South and Pradeep walks East, the distance between the two would keep on increasing. Hence, minimum distance cannot be 40 km in Scenario II.
Scenario III : Since, Devanand walks West and Pradeep walks East, the distance between the two would keep on increasing. Hence, minimum distance cannot be 40 km in Scenario III.
Hence, option (a) is the correct answer.