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08 Jan 2021, 07:13
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (03:11) correct
35%
(02:57)
wrong
based on 176
sessions
History
Date
Time
Result
Not Attempted Yet
On Sunday John left the place A for B at 3:30 am and on the same day Carsten started from B towards A at 8:30 am. They met each other at 12:30 pm. After meeting each other they took equal amount of time to reach their respective destinations. At what time did they reach their respective destinations?
A. 6:00 pm
B. 6:30 pm
C. 7:00 pm
D. 7:30 pm
E. 8:00 pm
Are You Up For the Challenge: 700 Level Questions
A. 6:00 pm
B. 6:30 pm
C. 7:00 pm
D. 7:30 pm
E. 8:00 pm
Are You Up For the Challenge: 700 Level Questions
08 Jan 2021, 12:32
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Distance travelled by John till 12:30= j*9
Distance travelled by Carsten till 12:30= c*4
\(\frac{j*9}{c} =\frac{c*4}{j} \)=t = time to reach their respective destinations after first meeting
\(\frac{j^2}{c^2 }= \frac{4}{9}\)
\(\frac{j}{c}= \frac{2}{3}\)
3j=2c
\(t=\frac{9j}{c}= \frac{6c}{c }= 6\)
B
Distance travelled by Carsten till 12:30= c*4
\(\frac{j*9}{c} =\frac{c*4}{j} \)=t = time to reach their respective destinations after first meeting
\(\frac{j^2}{c^2 }= \frac{4}{9}\)
\(\frac{j}{c}= \frac{2}{3}\)
3j=2c
\(t=\frac{9j}{c}= \frac{6c}{c }= 6\)
B
Bunuel
19 Jan 2021, 10:18
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Bunuel
Solution:
Let the rate of John be x and the rate of Carsten be y. When they met at 12:30pm, John had been traveling for 9 hours and Carsten had been traveling for 4 hours; thus they covered distances of 9x and 4y, respectively. After meeting, John has a distance of 4y to travel, which he will complete in 4y/x hours. Similarly, Carsten has a distance of 9x to travel and he will cover this distance in 9x/y hours. We are told that it took equal time for the two to reach their destinations; thus:
4y/x = 9x/y
4y^2 = 9x^2
2y = 3x or 2y = -3x
Since x and y are rates, neither can be negative; thus we can discard the possibility of having 2y = -3x.
Recall that it takes John 4y/x hours to complete his journey. Rewriting 4y/x = 12y/3x and substituting 2y = 3x, we see that it took John 12y/2y = 6 hours to reach his destination. Since they met at 12:30pm, John will reach his destination at 12:30pm + 6 hours = 6:30pm.
Notice that we will obtain the same result if we use Carston’s time of 9x/y (in which case we would rewrite 9x/y as 18x/2y and replace 2y by 3x).
Answer: B
I know that's picky, but when you deal with DS and other DI section issues of "can I even solve this?" it's important to hold out for those details. As written, this question has no answer! 
