Question
Consider a square ABCD. EFGH is another square obtained by joining the midpoints of the sides of the square ABCD where E, F , G amd H are the midpoints of AB, BC, CD and DA respectively. Lakshman and Kanika start from points B and D respectively at speeds ‘l’ kmph and ‘k’ kmph respectively and travel towards each other along the sides of the square ABCD. Jagadeesh starts from Point E and travels along the Square EFGH in the anti-clockwise direction at ‘j’ kmph. Lakshman and Kanika meet for the second time at H where Jagadeesh also meets them for the first time. If l : k : j is 1: 3 : 5√2 then the distance travelled by Jagadeesh is
CAT 2021
Correct option is
Explanatory Answer :
lakshman starts from point B at speed "l" kmph
kanika start from D at speed "k" kmph
and they both travel towards each other along the sides of the sqaure ABCD . and they are at a distance of 4a from each other .
as they are diametrically opposite points , the relative distance would be 4a irrespective of the directions they choose to travel in
so , to meet for the first time , they would have travelled a distance of 4a together
to meet the second time , they would have covered 8a distance together . essentially , between them , they would have cover the entire perimeter of square to meet again
so , by the time they meet for the second time , they would have covered 12a together ,
the speed are in the ratio 1:3 . so , laxman would have travelled 3a and kanika would have travelled 9a
and laxman travels in the direction BADC while kanika in the direction DABC.
they will meet at E for the first time and at H for the second time
at the same time jagdish travels along the square EFGH in the anticlockwise direction at "j" kmph and meet laxman and kanika .
while jagdish meets the other two for the first time , and we dont know about the laps
the ratio of laxman speed to that of jagdish is so they would have travel in the same direction
so , laxman travel the distance of 3a and jagdish should have travelled to reach H
hence jagdish travel 52a to reach H, heance ans is
so A is the correct option
