Discussion
Anil has a rectangular farm and he builds a road along the border of the farm from outside. The road is 5m wide and has an area of 600 m2. What is ratio of breadth and length of the farm?
Answer: D
The road runs outside the farm, so it forms a border of width 5 m around a rectangle \( l \times b \).
\[ \text{road area} = (l + 10)(b + 10) - lb = 10l + 10b + 100 \]
\[ 600 = 10(l + b) + 100 \quad\Longrightarrow\quad l + b = 50 \]
This fixes only the sum of the two dimensions. The pairs \( 25 \times 25 \), \( 20 \times 30 \) and \( 10 \times 40 \) all satisfy it and give different ratios, so the ratio cannot be determined.
A second independent fact - the farm's area or perimeter - would be needed to pin the shape down.
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