Question

The cost of fencing a circular field at the rate Rs $24$ per metre is Rs $5280$. The field is to be ploughed at the rate of Rs $0.50$ per $m^2$. Find the cost of ploughing the field. (Take $\pi =22/7$)

• A. Rs. $1278$
• B. Rs. $1437$
• C. Rs. $1925$
• D. Rs. $2870$

Answer 1

The correct option is C Rs. $1925$

We have,
Rate of fencing $=$ Rs $24$ per metre and, Total cost of fencing $=$ Rs $5280$

Length of the fence $=\frac{Totalcost}{Rate}=\frac{5280}{24}$ metre $=220$ metre.

$\Rightarrow$Circumference of the field $=220$ metres.

$\Rightarrow 2\pi r=220,$ where $r$ is the radius of the field

$\Rightarrow 2\times \frac{22}{7}\times r=220$

$\Rightarrow r=\frac{220\times 7}{22\times 2}=35$ metres

$\therefore$ Area of the field $=\pi r^2$

$\Rightarrow$ Area of the field $=\frac{22}{7}\times 35\times 35m^2=22\times 5\times 35m^2$

It is given that the field is ploughed at the rate of Rs $0.50$ per $m^2$

$\therefore$ Cost of ploughing the field = Rs $(22\times 5\times 35\times 0.50)=$ Rs $1925$