Latest Microsoft Aptitude Question SOLUTION: Two vehicles A and B leaves from city Y to X. A overtakes B at 10:30 am and reaches city C at 12:00 pm. It waits for 2 hrs and return to city Y. On its way it meets B at 3:00 pm an

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(#M40038888) MICROSOFT Category question Time and Distance Keep an EYE

Two vehicles A and B leaves from city Y to X. A overtakes B at 10:30 am and reaches city C at 12:00 pm. It waits for 2 hrs and return to city Y. On its way it meets B at 3:00 pm and reaches city Y at 5:00 pm. B reaches city X, waits for 1hr and returns to city Y. Afer how many hours will B reach city Y from the time A overtook him fro the first time?

1) 50 hrs
2) 49.5 hrs
3) 41.5 hrs
4) 37.5 hrs

Asked In Microsoft sourav chandan (9 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

ashvini kumar  (9 years ago)

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)

Is this solution Helpfull? Yes (31) | No (2)  

M.ARUN  (9 years ago)

is this a tough question?

Is this solution Helpfull? Yes (8) | No (1)  

moumita chakraborty  (8 years ago)

Let the distance between City X and Y be D
As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00

So it takes him 3 hours to cover distance D.

Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.

Now see,
A takes 3 hrs takes to cover distance D
so in 1.5 hrs A will cover D / 2 distance

Now see another part -
"On its way, it meets B at 3 PM and reaches Y at 5 PM."
Given that - B leaves City Y at 2 PM
So distance covered by A in 1 hr (3 - 2) = D / 3

Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is

D / 2 [when they first overtake] - D / 3 [when they again overtake]
= D / 6

Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )
=1.5 + 2 + 1
=4.5

so to cover D / 6 distance B took 4.5 hr
to cover D distance B will take (4.5 * 6)
= 27 hr.

Now "After how many hours will B reach to Y from the time A overtook him."
Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)
= 13.5 + 1 + 27
= 41.5

Is this solution Helpfull? Yes (2) | No (2)  

Niveditha Ravichandran  (9 years ago)

@ASHVINI KUMAR
how did you get the halt time for 1hr pls explain

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Rajashekhar  (9 years ago)

@Niveditha Ravichandran.....its given in the question " B reaches city X, waits for 1hr and returns to city Y"

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UMAIR SIDDIQUI  (8 years ago)

explain
it

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Rachit Chhabra  (6 years ago)

It should be reaches city X at 12:00 pm and not city C

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