Question

A river of 5 $\text{m}$ width and 2 $\text{m}$ depth flows with a speed of 20 $\text{km/hr}$. Water from this river is used to irrigate a field of area $x{\text{m}}^2$. The field is filled with water to a height of 0.5 $\text{m}$. If it takes 30 minutes to irrigate the field, then find $x$.

• A. $2,00,000m^2$
• B. $200m^2$
• C. $4,00,000m^2$
• D. $400m^2$

Answer 1

The correct option is A $2,00,000m^2$

Given: Width of the river = 5 m
Depth of the river = 2 m
Area of the field = $xm$
Height to which water is filled in the field = 0.5 m
Speed of water flow = 20 km/hr
$\Rightarrow$ In 1 hour water covers 20 km.
$\therefore$ In 30 minutes, water covers 10 km i.e. 10000 m.
Now, volume of water from river = Volume of the water on field
$\Rightarrow$ 10000 m $\times$ 5 m $\times$ 2 m = $x\times$ 0.5 m
$\Rightarrow$ 1,00,000 = $x\times$ 0.5
$\Rightarrow x$ = $\frac{1,00,000}{0.5}$ = $2,00,000m^2$