Question : The cost of levelling a circular field at 50 paise per square metre is Rs. 7,700. The cost (in Rs.) of putting up a fence all around it at Rs. 1.20 per meter is:
Option 1: Rs. 132
Option 2: Rs. 264
Option 3: Rs. 528
Option 4: Rs. 1056
Correct Answer: Rs. 528
Solution :
The cost of levelling it at 50 paise per square metre.
Rs. 0.5 per square meter for Rs. 7700.
Let the radius of the circular field be $r$.
The area of the circular field $= \pi r^2 $
So, according to the question
$\pi r^2 \times 0.5 = 7700 $
⇒ $r^2 = \frac{7700}{\pi \times 0.5}$
⇒ $r^2 = \frac{7700}{\frac{22}{7} \times 0.5}$
⇒ $r^2 = 4900$
⇒ $r = \sqrt{4900}$
⇒ $r = 70 \;\mathrm{metre}$
The circumference of the circular field,
$ = 2 \pi r = 2 \times \frac{22}{7} \times 70 = \frac{44}{7} \times 70 = 440 \;\mathrm{metre}$
The cost of putting up a fence around the circular field at Rs. 1.20 per metre.
The cost of fence = Circumference × Cost per metre
⇒ The cost of fence = 440 × 1.2 = Rs. 528
Hence, the correct answer is Rs. 528.
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