Question : The length and breadth of a rectangular field in the ratio of $7:4$. A path $4\operatorname{ m }$ wide running all around outside has an area of $416\operatorname{ m^2 }$. The breadth (in $\operatorname{m }$) of the field is:
Option 1: 28
Option 2: 14
Option 3: 15
Option 4: 16
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Correct Answer: 16
Solution : If a path of $x$ m wide runs around a rectangular field having $l$ as the length and $b$ as the breadth then, Area of path = $2x(l+b+2x)$ We have the length and breadth of a rectangular field in the ratio of $7:4$. A path $4\operatorname{ m }$ wide running all around outside has an area of $416\operatorname{ m^2 }$. Let the length and breadth of a rectangular field be $7y$ and $4y$. Area of the path = $2×4(7y+4y+2×4)$ $⇒416=8(7y+4y+8)$ $⇒11y=44$ $⇒y=4$ So, the breadth of the rectangular field $= 4y=16\operatorname{ m}$ Hence, the correct answer is 16.
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