Xavier Aptitude Test 2015 Paper

Question : 66 of 113

Marks: +1, -0

Devanand's house is 50 km West of Pradeep's house. On Sunday morning, at 10 a.m., they leave their respective houses.
Under which of the following scenarios, the minimum distance between the two would be 40 km ?
Scenario I : Devanand walks East at a constant speed of 3 km per hour and Pradeep walks South at a constant speed of 4 km per hour.
Scenario II : Devanand walks South at a constant speed of 3 km per hour and Pradeep walks East at a constant speed of 4 km per hour.
Scenario III : Devanand walks West at a constant speed of 4 km per hour and Pradeep walks East at a constant speed of 3 km per hour.

Scenario I only
Scenario II only
Scenario III only
Scenario I and II
None of the above

Validate

Solution:

(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.

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