The speed of a boat in still water is 50 percent more than its speed upstream. If the boat takes 20 minutes to reach point Q from point P downstream, how long will it take to reach point P from point Q upstream?
Show answer & explanation
Correct answer: A
Explanation
The Correct answer is Option 1 i.e. 40 min.
Let the speed of the boat be B and the speed of the stream be S;
So,
Speed upstream = B - S
Speed downstream = B + S
According to the question:
B = 1.5 × (B - S)
⇒ B = 1.5 × B - 1.5 × S
⇒ 0.5 × B = 1.5 × S
⇒ B = 3 × S
We know that,
Downstream speed = B + S and time taken is 20 minutes;
Let D be the distance between P and Q,
D = (B + S) × Time
⇒ D = (3S + S) × 20/60
⇒ D = 4S × 1/3
⇒ D = 4/3S
Now, to find the time taken in upstream, from Q to P:
In Upstream, the boat speed is B - S and time is T
D = (B - S) × T
⇒ 4/3S = (3S - S) × T
⇒ 4/3S = 2S × T
⇒ T = 4/3S/2S
T = 2/3 hours
Now, converting hours into minutes:
⇒ T = 2/3 × 60
⇒ T = 40 minutes
So, it will take 40 minutes to reach point P from Q in upstream.