Question

The length and breath of a plot are in the ratio of 5:3 and its perimeter is 320m. A 3m wide path runs along the inside boundary. Find the cost of paving the path at Rs. 2.5 per sq m. ​

Answer 1

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$let \: the \: length \: be \: 5x \\ let \: the \: breadth \: be \: 3x \\ and \: perimeter \: of \: plot \: is \: 320m \: ( \: given \: ) \\ perimeter \: of \: rectangle \: = 2 \: ( \: l + b \: ) \\ = > \: 2 \: (5x + 3x \: ) \: = 320 \\ = > \: 10x + 6x = 320 \\ = > 16x = 320 \\ = > x = \frac{320}{16} \\ = > x = 20 \\ so \: length = 5x = 5 \times 20 = 100 \\ and \: breadth \: = 3x = 3 \times 20 = 60 \\ then \: \\ \: \: area \: of \: outer \: part \: = 100 \times 60 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6000 \\ area \: of \: inner \: part \: = \: 100 - 3 \times 60 - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 97 \times 57 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5529 \\ = > area \: of \: path = area \: of \: outer \: part - area \: of \: inner \: part \\ = > area \: of \: path \: = 6000 - 5529 \\ = > area \: of \: path \: = 471 \\ the \: cost \: of \: paving \: the \: path \: at \: rs \: 2.5square \: metre \\ = > 471 \times 2.5 \\ = > 117.5$
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