If the total cost of mowing a circular field at the rate of ₹1.20 per square metre is ₹4,620, then the cost of fencing the field at the rate of ₹4 per metre is :

1. ₹ 878

2. ₹ 880

3. ₹ 882

4. ₹ 884

Given,

Rate of mowing = ₹ 1.20 per square metre.

Total cost = ₹4,620

Area = $\dfrac{\text{Total cost}}{\text{Rate}}$

= $\dfrac{4620}{1.20}$ = 3850 m².

Let radius of circular field be r meters.

$\Rightarrow πr^2 = 3850 \\[1em] \Rightarrow \dfrac{22}{7} \times r^2 = 3850 \\[1em] \Rightarrow r^2 = \dfrac{3850 \times 7}{22} \\[1em] \Rightarrow r^2 = 1225 \\[1em] \Rightarrow r = \sqrt{1225} \\[1em] \Rightarrow r = 35 \text{ m}.$

Circumference of circle = 2πr

= 2 × $\dfrac{22}{7}$ × 35

= 220 m.

Cost of fencing = Circumference of field × Rate of fencing

= 220 × 4 = ₹ 880.

Hence, option 2 is the correct option.