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16 Sep 2024, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
56% (02:34) correct
44%
(03:02)
wrong
based on 138
sessions
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Trains A and B start traveling towards each other at the same time from stations X and Y, respectively, each moving at its own constant speed. Train A reaches station Y in 10 minutes, while train B takes 9 minutes to reach station X after meeting train A. What is the total time, in minutes, taken by train B to travel from station Y to station X?
A. 6
B. 8
C. 10
D. 12
E. 15
A. 6
B. 8
C. 10
D. 12
E. 15
Bunuel
use the meeting time formula here.
Lets assume x is the time that both took to meet.
Formula is, \(x = \sqrt{Time taken by A to Reach Y after meet * Time taken by B to reach X after meet}\)
Given - Train A reaches station Y in 10 minutes
Therefore, Time taken by A to Reach Y after meet = Total time - Meet time = 10 - x
and B takes 9 minutes to reach station X after meeting train A.
Therefore, \(x = \sqrt{(10-x) * 9}\)
\(x^2 = (10-x)9\)
solving,
\(x^2 +9x - 90 = 0\)
Get the value for x. Here x you will get 6 min.
Now the total time, in minutes, taken by train B to travel from station Y to station X = x + 9 = 6+9 = 15 min.
Answer is E.
Derivation for the formula mentioned-
I will draw schematic for this
(X) A>-------------------meeting point p----------------------<B (Y)
let ap be the distance covered by A during meet similarly bp is distance covered by B during the meet.
i will keep variable x as same for time taken by them to meet.
Now as we know Distance = Speed*Time
ap = A*x and bp = B*x (Here A and B are speeds for train A and B)
Both trains after meet moving towards their respective destinations
So now A will cover the distance distance bx and B will cover distance ax and lets take time they took to cover those distances after meeting at p are m and n respectively for both A and B
Therefore,
ap = A*x = B*n and bp = B*x = A*m
now from here we get \(\frac{A}{B} = \frac{n}{x} = \frac{x}{m}\)
from here just take these two \(\frac{n}{x} = \frac{x}{m}\)
solve, \(x^2 = m*n\)
which means \(x = \sqrt{mn} = \sqrt{Time taken by A to Reach Y after meet * Time taken by B to reach X after meet}\)
Hope this helps
General Discussion
16 Sep 2024, 05:18
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IMO E
X- - - - ————- ——Y
D= x miles
A. B
Va= x/10. Vb= x/(t+9) where t is the time taken to meet each other
GAP= (Va+Vb)* Time taken to meet each other
—-> x= [(x/10) +(x/(t+9))]*t
1= ((1/10)+1/(t+9))*t
10t+90 =t(t+19)
t^2 +9t-90 =0
t=6 or t=-15 only the positive value is taken
Thus the time to travel from Y to X is t+9 = 6+9=15
Posted from my mobile device
X- - - - ————- ——Y
D= x miles
A. B
Va= x/10. Vb= x/(t+9) where t is the time taken to meet each other
GAP= (Va+Vb)* Time taken to meet each other
—-> x= [(x/10) +(x/(t+9))]*t
1= ((1/10)+1/(t+9))*t
10t+90 =t(t+19)
t^2 +9t-90 =0
t=6 or t=-15 only the positive value is taken
Thus the time to travel from Y to X is t+9 = 6+9=15
Posted from my mobile device
