Aptitude - Simplification - Discussion

Discussion :: Simplification - General Questions (Q.No.15)

15. 

David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

[A]. 19
[B]. 28
[C]. 30
[D]. 37

Answer: Option C

Explanation:

Suppose their paths cross after x minutes.

Then, 11 + 57x = 51 - 63x       120x = 40

x = 1
3

Number of floors covered by David in (1/3) min. = 1 x 57 = 19.
3

So, their paths cross at (11 +19) i.e., 30th floor.


Geeni said: (Jan 12, 2011)  
Consider david to be stationary then difference speed is
= 57+63 floor/minute
= 120f/m.

Total difference of floor is 51-11=40 floors.

Therefore minutes is (120f/m) /40f=1/3m.

So 11 + (1/3) * 57 = 51-(1/3)*63 = 30.

Nje said: (Aug 16, 2011)  
Geeni you're a genius.

Rehana said: (Oct 14, 2011)  
Its 40f/120f/m=1/3min

Hardik said: (Aug 22, 2012)  
@Geeni

Please explain last step
11+(1/3)*57=51-(1/3)*63

Deepti said: (Sep 1, 2013)  
Can someone explain how you got 11+(1/3)*57b = b51-(1/3)*63?

Subhadip said: (Sep 29, 2013)  
Just visualize the problem solve & understand last step.

Radhika K R said: (Dec 24, 2013)  
We can also predict it though an train problem, two people who are travelling opposite direction:

Here total speed will be 63+57 (f/m) =120 f/m.

Total distance will be subtracted 51 -11.

So the time they will meet will be 40/120=1/3 min.

So the distance will be for their meet will be:

11+57*1/3= 30.

or

51-63*1/3=30.

Amit said: (Sep 17, 2014)  
@Geeni.

Just implemented the concept of relative velocity.

1/3 is time at which david and albert meet. So he multiply that time to the velocity of david and calculate the distance travelled by david and finally he added that distance to david's initial position.

Mani said: (Oct 14, 2014)  
s = d/t.
In this problem time travel is same for both=> d1/s1 = d2/s2.

Lets assume they cross the paths at yth floor.
(y-11)/57=(51-y)/63.

Solve this,
y=30.

Mukesh said: (Nov 13, 2015)  
@Mani.

You are cool, this is the best way and the easiest way.

Rabia said: (Jan 3, 2016)  
@Geeni.

Please explain last step.

Kumar said: (Sep 5, 2016)  
@Mani, How is Y value same for both but different in speeds?

Saba Khan said: (Oct 9, 2016)  
You are very talented @Geeni.

Prashant said: (Oct 10, 2016)  
@Kumar

Because at Yth position both of them meet so the distance from David is (y-11) and that of Albert is (51-y).

Anshi said: (Sep 15, 2017)  
@Mani.

Good one.

Shivani said: (Aug 3, 2018)  
Thanks for your solution @Mani.

Raj said: (Aug 21, 2018)  
Thank you so much for explaining the solution of this.

Albert Einstein said: (Sep 9, 2018)  
Well said, thanks for your explanation @Radhika K R.

Samiksha said: (Dec 17, 2018)  
Can anybody make me understand this question? Please.

Sandeep said: (Dec 31, 2018)  
If David stationary then how we can add 57+63.

57 is David speed per min.

Diwakar Ramachandra said: (Apr 29, 2019)  
Since, both X and Y are traveling in opposite directions, their relative speed = (57+63) floor/minute = 120f/m.

Total distance between X an Y in terms of floors = 51-11=40 floors.

Therefore, time taken to cross each other = Distance/Speed = 40/120= 1/3 minutes.
Distance (floors) traveled by X in 1/3 minutes = Speed x Time = 57 x 1/3 = 19 floors.
So, X would have travelled to 11 + 19 = 30 floors when the meet/cross each other.

Akshatha said: (Nov 10, 2019)  
Can anyone tell me the problem meaning step by step?

Akshay said: (Jun 15, 2020)  
Taking the ratios 57:63
We get 19:21.

David is in 11th floor. David is going upward direction. So 11+19=30th floor.
Otherwise, Albert is in the 51st floor and he goes downward. So 51-21=30th floor.

Monsahab said: (Jul 29, 2020)  
Anyone, explain the Solution, please.

Finara said: (Jul 31, 2020)  
David's starting position = 11th floor.
Albert's = 51st,

So, distance covered by david till the point they meet= x
and for Albert= (40-x)

Speed of David = 57 floors/minute
and for Albert = 63 floors/minute.

As time taken by both will be same equation becomes:
(x/57) = (40-x)/63
x = 19.

Thus, answer is (11+19) or (51-21) => 30th Floor.

Anil Sah said: (Dec 22, 2020)  
Not understanding, Please anyone help me to get it.

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