Question

two vehicles A and B leave from Y to x . A overtake B at 10.30 am and reaches city X at 12.00 pm .it wait for 2 hour and return to city Y.on its way it meet B at 3;00 pm and reaches city X . waits for 1 hour and return to city Y .After how many hour will B reaches city Y from the time A overtook him for the first time?
a} 50 hour
b] 41.5 hour
c]49.5 hour
d]37.5 hour; two vehicles A and B leave from Y to x . A overtake B at 10.30 am and reaches city X at 12.00 pm .it wait for 2 hour and return to city Y.on its way it meet B at 3;00 pm and reaches city X . waits for 1 hour and return to city Y .After how many hour will B reaches city Y from the time A overtook him for the first time?; a} 50 hour; b] 41.5 hour; c]49.5 hour; d]37.5 hour

Answer 1

suppose distance b/w x&y=a
since after reaching at x;A start at 2:00 and reach at y at 5:00
speed of A=a/3 
since in coming from y to X A overtook B at 10:30 and reach at X at 12:00
so in 1.5 hours it will cover half distance of YX=a/2
again in returning from X to y it meet B at 3:00 so distance from X to here=a/3
means distance from Y to 2nd meet of B=2a/3
so B covered distance in 4.5 hours(3:00-10:30)=2a/3-a/2=a/6
since B covers a/6 in 4.5 hours
so B will cover distance a in (4.5/(a/6))*a=27 hours
after meet to A 1st time ,B covers total distance=a/2+a(wait at X)
so total time =27(from X to Y)+27/2(after meeting A 1st time to reach at X)+1(halt at X)=41.5
so correct option is (3)