Let us draw the rectangle.
Now, definitely, three sides should be fenced at Rs 100/ft, and one side should be fenced at Rs 200/ft.
In this question, we are going to assume that the $\L$ is greater than $\B$.
Hence, the one side painted at Rs 200/ft should be $\B$ to minimize costs.
Hence, the total cost $= 200\B + 100\B + 100\L + 100\L = 300\B + 200\L $
Now, $\L × \B = 60000 $
$\B = 60000/\L$
Hence, total cost $= 300\B + 200\L = 18000000/\L + 200\L $
To minimize this cost, we can use $\AM>=\GM$
$18000000/ \L + {200 \L}/2 ≥ 2 √{18000000/\L × 200\L }$
$18000000/\L + 200\L ≥ 2√{18000000 × 200}$
$18000000/\L + 200 \L ≥ 2× 60000$
Hence, minimum cost $= Rs 120000$.