Question

The length and breadth of a rectangular field are
in the ratio 5:3. If the cost of reaping the field at
85 paise per square metre is Rs 624.75, find the
cost of fencing it at the rate of Rs 4 per metre. it ans is 《Rs 448》.​

Answer 1

$\huge{ \bold{ \red{question : - }}}$

The length and breadth of a rectangular field are

in the ratio 5:3. If the cost of reaping the field at

85 paise per square metre is Rs 624.75, find the cost of fencing it at the rate of ʀꜱ 4 ᴩᴇʀ ᴍᴇᴛʀᴇ

$\huge{ \bold{ \blue{ solution : }}}$

$\huge{ \bold{l : b = 5 : 3}}$

$\huge{ \bold{ \frac{l}{b} = \frac{5}{3} = > l = \frac{5}{3} b}}$

$\huge{ \bold{total \: cost \: of \: reabing}}$

$\huge{ \bold{624.75 = 85 \times (l \times b)}}$

$\huge{ \bold{ \frac{62475}{100 \times 85} = l \times b}}$

$\huge{ \bold{ 7.35 = l \times b}}$

$\huge{ \bold{7.35 = \frac{5}{3} {b}^{2} }}$

$\huge{ \bold{ {b}^{2} = \: \frac{3 \times 735}{5 \times 100} = \frac{3 \times 147}{10 \times 10} = \frac{7 \times 3}{10} }}$

$\huge{ \bold{b = \frac{21}{10} }}$

$\huge { \bold{ l = \frac{5}{3} \times \frac{21}{10} = \frac{7}{2} }}$

$\huge{ \bold{ answer \: = \: \frac{7}{2} }}$

Answer 2

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) The length and breadth of a rectangular field are in the ratio 5:3 . If the cost of reaping the field at 85 paise per square metre is Rs 624.75 , Find the cost of fencing it at the rate of Rs 4 per meter.

${\huge{\underbrace{\underline{\rm{Answer\checkmark}}}}}$

$\frak{Given}\begin{cases}\rm{Length:Breadth=\bf{5:3\:.}}\\ \rm{Rate\:of\:reaping=\bf{85\:p\:per\:m^2\:.}}\\ \rm{Cost\:of\:reaping=\bf{Rs\:624.75\:.}}\\ \rm{Rate\:of\:fencing=\bf{Rs\:4\:per\:meter\:.}}\end{cases}$

${\bf{\underline{\bigstar\:To\;Find\::-}}}$ The cost of fencing.

${\bf{\large{\underline{\bigstar\:Solution:}}}}$

• Since we are given with the cost and rate of reaping the field, we would use it, along with the given ratio of length and breadth, to get the value of length and breadth.

• After finding the length and breadth, we would find the perimeter of the field and multiply it with the given rate of fencing so as to get the cost.

• In Reaping , the area of field is involved, whereas in fencing perimeter of the field is involved .

${\textit{\textbf{Finding\:Length\:and\:Breadth:}}}$

We know,

• Length : Breadth = 5:3

Let the ratios be 5x and 3x .

it means ,

• Length = 5x
• Breadth = 3x

So,

$\mapsto \sf \: area _{field} = length \times breadth \\ \\ \mapsto \sf \: area _{field} = 5x \times 3x \\ \\ \sf \mapsto \boxed{ \bf{ area _{field} = 15 {x}^{2} }}$

Now ,

We know

• Rate of reaping = 85 p = 0.85 Rs

and ,

• Cost of reaping = 624.75 Rs

$\leadsto \sf \: cost _{ \: ( \: reaping \: )} = rate _{ \: ( \: reaping \: )} \times area_{ \: ( \: field \: )} \\ \\ \leadsto \sf \: \cancel{624.75} \: rs = \cancel{0.85 }\: rs \times 15 {x}^{2} \\ \\ \leadsto \sf \: \cancel{735} = \cancel{15} {x}^{2} \\ \\ \leadsto \sf \: {x}^{2} = 49 \\ \\ \leadsto \sf \: x = \sqrt{49} \\ \\ \leadsto \boxed{ \underline{ \bf{x = 7}}}$

So ,

$\bull \rm \: length = 5x = 5 \times 7 \: m \\ \\ \underline{ \boxed{ \tt{length = \bf{ \blue{35 \: m}}}}}$

$\bull \rm \: breadth = 3x = 3 \times 7 \: m \\ \\ \underline{ \boxed { \tt{breadth = \bf{ \purple{21 \: m}}}}}$

${\textit{\textbf{Finding\:Final\:Answer:}}}$

Before finding the cost of fencing , we have to find the perimeter of the field.

$\colon \implies \sf \: perimeter _{ \: ( \: field \: )} =2 \times \{ length + breadth \} \\ \\ \colon \implies \sf \: perimeter _{ \: ( \: field \: )} = 2(35 + 21) \: m \\ \\ \colon \implies \sf \: perimeter _{ \: ( \: field \: )} = 2 \times 56 \: m \\ \\ \colon \implies \underline{ \boxed{ \tt{perimeter _{ \: ( \: field \: )} = \bf {\pink{112 \: m}} \: }}}$

Now ,

We know ,

• Rate of fencing = Rs 4 .

So,

$\colon \rightarrow \sf \: cost _{ \: ( \: fencing \: )} = rate _{ \: ( \: fencing \: )} \times perimeter _{ \: ( \: field \: )} \\ \\ \colon \rightarrow \sf \: cost _{ \: ( \: fencing \: )} = 4 \times 112 \: Rs \\ \\ \colon \rightarrow \underline{ \overline{ \boxed{ \rm{cost _{ \: ( \: fencing \: )} = \bf{ \red{448 \: Rs}}}}}}$

So,

The Cost of fencing the field would be Rs 448 .

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