Question

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A carpenter puts a beading around a wooden table whose length and breadth are in the ratio 7: 3.
If the total cost of putting the beading is 1200 at the rate of 530 per metre, find the dimensions​

Answer 1

GIVEN:-

• $\rm{Length\:of\:table = 7x}$

• $\rm{Breadth\:of\:table = 3x}$

• $\rm{Total\: Cost\:of\:beading = 1200}$

• $\rm{Rate\:of\:Per\metre = 30}$.

TO FIND:-

• The Dimensions of Wooden table.

HOW TO SOLVE:-

• In the question it is given that total cost is 1200at rate of 30 Per metre.

• If we divide 1200 by 30 then we can find the total area of table.

So,

$\implies\rm{ Total\:area = \dfrac{Total\:Cost}{Cost\:per\:m}}$.

$\implies\rm{Total\:area = \dfrac{1200}{30}}$

$\implies\rm{Total\:area = 40m}$

Now,

Total Area covered by beeding = Perimeter of table

$\implies\rm{Area\:of\:Wooden\:table = 2(L + B)}$

$\implies\rm{ 40m = 2(7x+3x)}$

$\implies\rm{ 40m = 20x}$

$\implies\rm{ x = 2}$.

Therefore,

Length of Table = 7x = 14

Breadth of Table = 3x = 6.

Answer 2

$\bf{\underline{Question:-}}$

A carpenter puts a beading around a wooden table whose length and breadth are in the ratio 7: 3.

If the total cost of putting the beading is 1200 at the rate of 530 per metre, find the dimensions.

$\bf{\underline{Solution:-}}$

• total cost = 1200

• rate = ₹ 30/metre

$\bf{\underline{Therefore:-}}$

• total distance covered by beading = 1200/30 = 40 metre

ratio = 7:3

Let,

• common factor be x then,

• ratio = 7x : 3x

• Total area covered by beading = perimeter of table

→ 40 m = 2(7x + 3x)

→ 40 = 20x

→ x = 2

$\bf{\underline{Hence:-}}$

• length of table = 7x = 7×2 = 14 metre

• breadth of table = 3x = 3 × 2 = 6 metre