Subject: General Aptitude · Chapter: Boats and Streams · Exam: 2007 · Marks: · Difficulty:
A boat goes 8 km upstream and then returns. Total time taken is 4 hrs 16 minutes. If the velocity of current is 1 km/hr, find the actual velocity of the boat.
Answer
Answer (as printed):
Explanation
Let the actual velocity of the boat be $x \mathrm{km} / \mathrm{hr}$. Then, Speed downstream $=(x+1) \mathrm{km} / \mathrm{hr}$; Speed upstream $=(x-1) \mathrm{km} / \mathrm{hr}$. $$\begin{aligned} & \therefore \quad \frac{8}{x+1}+\frac{8}{x-1}=4 \frac{16}{60}=4 \frac{4}{15}=\frac{64}{15} \Leftrightarrow \frac{(x-1)+(x+1)}{(x+1)(x-1)}=\frac{8}{15} \Leftrightarrow 30 x=8\left(x^{2}-1\right) \\ & \Leftrightarrow 4 x^{2}-15 x-4=0 \Leftrightarrow 4 x^{2}-16 x+x-4=0 \Leftrightarrow 4 x(x-4)+(x-4)=0 \\ & \Leftrightarrow(x-4)(4 x+1)=0 \Leftrightarrow x=4 . \end{aligned}$$ Hence, actual velocity of the boat = 4 km/hr.