Question

Vihang rowed upstream $48$kms. and back in $14$ hourse. He can row $4$kms. downstream in the same time as $3$kms. Find the flow of the stream

• A. $1$km/hr.
• B. $0.5$km/hr.
• C. $0.75$km/hr.
• D. $1.5$km/hr.

Answer 1

The correct option is A $1$km/hr.

Vihang rowed upstream 48 kms. and back in 14 hours. He can row downstream 4 kms in the same time as 3 kms. upstream.

We know, $\text{speed}=\frac{\text{distance}}{\text{time}}$

$\therefore$ Speed downstream $=\left(\frac{4}{x}\right)km/hr.$

[ where we let, het move 4 km downstream x hours]

$\therefore$ Speed upstream $=\left(\frac{3}{x}\right)km/hr.$

According to the question,

$\frac{48}{4/x}+\frac{48}{3/x}=14$

So, $\frac{48x}{4}+\frac{48x}{3}=14$

or, $12x+16x=14$

or, $x=\frac{14}{28}$

or, $x=\frac{1}{2}$

Hence , speed of downstream $=\frac{4}{1/2}=8km/hr.$

and speed of upstream $=\frac{3}{1/2}=6km/hr.$

We know, speed of the stream is given by

$\frac{1}{2}$ (downstream speed - upstream speed)

Hence, speed of the stream $=\frac{1}{2}(8-6)km/hr.=1km/hr.$

$\therefore$ option A is correct.