A motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours.
A motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed it can travel 32 km downstream and 12 km upstream in 10 hours. The speed of the stream is:
एक मोटरबोट किसी निश्चित गति से चलते हुए 24 किमी धारा के विपरीत (अपस्ट्रीम) तथा 40 किमी धारा के अनुकूल (डाउनस्ट्रीम) दूरी 17 घंटे में तय करती है। उसी गति से वह 32 किमी धारा के अनुकूल तथा 12 किमी धारा के विपरीत दूरी 10 घंटे में तय करती है। धारा की गति कितनी है?
Detailed Solution & Logic
3 km/h
Let the speed of the boat in still water be $b$ km/h and the speed of the stream be s km/h.
$\frac{24}{b-s}+\frac{40}{b+s}=17$
$\frac{12}{b-s}+\frac{32}{b+s}=10$
Let,
$x=\frac{1}{b-s}, y=\frac{1}{b+s}$
Then,
$24x+40y=17$
$12x+32y=10$
$\Rightarrow 24x+64y=20$
Subtracting,
24y=3
$y=\frac{1}{8}$
So,
$b+s=8$
Also,
$12x+4=10$
$x=\frac{1}{2}$
So,
b-s=2
Therefore,
$s=\frac{(8-2)}{2}=3$ km/h.
Answer: 3 km/h
Similar Practice Questions
A policeman chases a thief.
A policeman chases a thief. The speed of the policeman and thief are 10 kmph...
Diya has to reach Surat, 804 km away, in 24 hours. The initial speed for 9 hours was 58 km/hr. For the next 162 km her speed was 54 km/hr. At what speed will she have to travel now to reach Surat in the stipulated time of 24 hours?
Diya has to reach Surat, 804 km away, in 24 hours. The initial speed for...
Pipe X can fill a tank in 60 hours while pipe Y can fill the tank in 72 hours. Both pipes are opened together for 20 hours. How much of the tank is left empty ?
Pipe X can fill a tank in 60 hours while pipe Y can fill the...
In a 100‑meter race, A covers a certain distance in 36
In a 100‑meter race, A covers a certain distance in 36 seconds and B covers...
Two athletes are participating in a race on a circular track of 220 m.
Two athletes are participating in a race on a circular track of 220 m. Ravi...
A man goes to Ahmedabad from Kolkata at a speed
A man goes to Ahmedabad from Kolkata at a speed of 9km/hr and returns to...
The speed of a stream is 9 km/h.
The speed of a stream is 9 km/h. A boat can go 56 km downstream...