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

A
B
C
D
##### 7.5 times the side of the square EFGH
Solution

Correct option is

(A)

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 $1:5sqrt{2}$ so they would have travel in the same direction

so , laxman travel the distance of 3a and jagdish should have travelled $3a*5sqrt{2}$ to reach H

hence jagdish travel 52a to reach H, heance ans is $7.5*sqrt{2}$

so A is the correct option