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Ncert exemplar solutions

CHAPTERS

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Let the speed of the stream be x km/hr.

And, the speed of the boat in still water = 5 km/hr

Speed of the boat upstream = (5 – x)km/hr

Speed of the boat downstream = (5 + x) km/hr

Time taken in rowing 40 km upstream = 40/(5-x) hrs

Time taken in rowing 40 km downstream = 40/(5+x) hrs

According to the question, we have

Time taken in 40 km upstream = 3 × Time taken in 40 km downstream

\therefore \frac{40}{5-x}=\frac{3 \times 40}{5+x} \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow-3 x+15=x+5 \\ \Rightarrow-3 x-x=5-15 \\ \Rightarrow-4 x=-10 \\ \Rightarrow x=\frac{10}{4}

⇒ x = 2.5 km/hr

Hence, the speed of stream is 2.5 km/hr.

Let the speed of the stream be x km/hr.

And, the speed of the boat in still water = 5 km/hr

Speed of the boat upstream = (5 – x)km/hr

Speed of the boat downstream = (5 + x) km/hr

Time taken in rowing 40 km upstream = 40/(5-x) hrs

Time taken in rowing 40 km downstream = 40/(5+x) hrs

According to the question, we have

Time taken in 40 km upstream = 3 × Time taken in 40 km downstream

\therefore \frac{40}{5-x}=\frac{3 \times 40}{5+x} \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow-3 x+15=x+5 \\ \Rightarrow-3 x-x=5-15 \\ \Rightarrow-4 x=-10 \\ \Rightarrow x=\frac{10}{4}

⇒ x = 2.5 km/hr

Hence, the speed of stream is 2.5 km/hr.

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