Anurag20589

MOST IMPORTANT QUESTIONS FOR CLASS 10 BOARDS    

1- A motor boat whose speed is 18km/h in still water takes 1 hour more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream.

Solution

Let the speed of the stream be x km/hr
Speed of the boat upstream = Speed of boat in still water - Speed of the stream
$\therefore$ Speed of the boat upstream = (18-x) km/hr
Speed of the boat downstream = Speed of the boat still water + Speed of the stream
$\therefore$ Speed of the boat upstream = (18+x) km/hr
Time of upstream journey = Time for downstream journey + 1 hr
$\therefore \frac{Distancecoveredupstream}{Speedoftheboatupstream}=\frac{Distancecovereddownstream}{Speedoftheboatdownstream}+1hr$
$\Rightarrow \frac{24km}{(18-x)}=1$
$\Rightarrow \frac{24}{18-x}-\frac{24}{18+x}=1$
$\Rightarrow \frac{432+24x+432+24x}{(18-x)(18+x)}=1$
$\Rightarrow 48x=324-x^2$
$\Rightarrow x^2+48x-324=0$
$\Rightarrow x(x+54)-6(x+54)=0$
$\Rightarrow (x+54)(x-6)=0$
$\Rightarrow x+54=0orx-6=0$
$\Rightarrow x=-54orx=6$
$\therefore$ x=6 (Speed of the stream cannot be negative)
Thus, the speed of stream is 6 km/hr.

2-A motor boat whose speed is 18km/h in still water takes 1 hour more to go 24km upstream  than to return downstream to the same spot. Find the speed of the stream.

Solution

Let the speed of the stream be x km/hr
Speed of the boat upstream = Speed of boat in still water - Speed of the stream
$\therefore$ Speed of the boat upstream = (18-x) km/hr
Speed of the boat downstream = Speed of the boat still water + Speed of the stream
$\therefore$ Speed of the boat upstream = (18+x) km/hr
Time of upstream journey = Time for downstream journey + 1 hr
$\therefore \frac{Distancecoveredupstream}{Speedoftheboatupstream}=\frac{Distancecovereddownstream}{Speedoftheboatdownstream}+1hr$
$\Rightarrow \frac{24km}{(18-x)}=1$
$\Rightarrow \frac{24}{18-x}-\frac{24}{18+x}=1$
$\Rightarrow \frac{432+24x+432+24x}{(18-x)(18+x)}=1$
$\Rightarrow 48x=324-x^2$
$\Rightarrow x^2+48x-324=0$
$\Rightarrow x(x+54)-6(x+54)=0$
$\Rightarrow (x+54)(x-6)=0$
$\Rightarrow x+54=0orx-6=0$
$\Rightarrow x=-54orx=6$
$\therefore$ x=6 (Speed of the stream cannot be negative)
Thus, the speed of stream is 6 km/hr.