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Bunuel
The speed of a boat in still water is 24kmph and the speed of the stream is 4kmph. The time taken by the boat to travel from A to B downstream is 36 minutes less than the time taken by the same boat to travel from B to C upstream. If the distance between A and B is 4 km more than the distance between B and C, what is the distance between A and B ?

(A) 56 km
(B) 86 km
(C) 110 km
(D) 112 km
(E) 120 km


Let \(d\) be the distance between B and C hence \(d+4\) is the distance between A and B

\(\frac{d +4}{24+4}\)= \(x- \frac{36}{60}\) (i)

\(\frac{d }{24-4}\)= \( x\) (ii)

24= Speed of boat
4= Speed of stream
\(x\)= time(h) taken to go from B to C upstream.

Solving (i) and (ii) for \(d \) we will be get \(d\)= 82 which is the distance between \(b\) and \(C \)
Hence the distance between \(a\) and \(b \) is = \(82+4=86\)

Ans= B.

Hope it's clear.
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Bunuel could you help me understand how is the answer option B 86 and not option A 56

I solved it as follows:
\(\frac{(x+4)}{28} = \frac{x}{20} - \frac{36}{60}\), where x = distance between B and C
\(\frac{x}{20} - \frac{(x+4)}{28} = \frac{3}{5}\)
On solving this, I get x = 52.
Hence the distance between A and B should be \(52 + 4 = 56\) which is option A

I tried to check my answer as well:

If the distance between A and B is 86, then the distance between B and C is 82.
Hence, the time difference between travelling from B to C and A to B = \(\frac{82}{20} - \frac{86}{28} = 1.03 hours = 61.8 mins\)
This contradicts the question where the time difference is 36 mins

Whereas if we take the distance between A and B as 56, then,
time difference = \(\frac{52}{20} - \frac{56}{28} = 0.6 hours = 0.6 * 60 = 36 mins\), which is correct according to the question

Could you please help me understand where am I going wrong?
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I was getting A as the answer, and I was wondering where I was going wrong. Thanks Scott for the explanation. I did the same way too
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ScottTargetTestPrep

Thank you for adding an expert opinion. I answered A as well and could not figure out what I had done wrong.

Posted from my mobile device
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ScottTargetTestPrep

Thank you for adding an expert opinion. I answered A as well and could not figure out what I had done wrong.

Posted from my mobile device

Response:

56 km is the correct answer for this question. I believe there is a typo with the OA for this question.
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