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
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