Question

Length of a box is four times its height and its breadth is 3 times its height. The cost of white washing the walls at the rate of rs4 per mis 26. Find the cost of tiling the floor at the rate of rs10 per m.
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Answer 1

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

❥ Length of a box is four times its height and its breadth is 3 times its height. The cost of white washing the walls at the rate of rs4 per mis 26. Find the cost of tiling the floor at the rate of rs10 per m.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

The cost of tiling the floor is ₹ 12.85.

$\Large{\underline{\underline{\bf{Given:-}}}}$

↠ Length

↠Cost

• Length of a box is four times its height and its breadth is 3 times its height.

• The cost of white washing the walls at the rate of ₹ 4 per m² is ₹ 6.

$\Large{\underline{\underline{\bf{To Find :-}}}}$

What is the Cost of tiling the floor ?

So , Here we go .

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

As we know height of the box is not given .

So , Let the height be " h "

Now According to the Question

Length and breadth would be :-

❥ Length = 4h ↠ 4 × Height

❥ Breadth = 3h ↠ 3 × Height

Applying the formula of Cuboid as the box is in cuboid shape

❥ Area of walls = (Total surface area) - (2 × Area of floor)

↠ 2( LB + BH + LH ) - 2LB

↠ 2( BH + LH )

↠ 2( 3h × h + 4h × h )

↠ 2(3h² + 4h²)

${\boxed{\bold{Therefore, \ the \ area \ of \ the \ wall \ is \ 14 \ h^{2} }}}}$

As per the given cost and rate of white washing

❥ Cost = Area × Rate

6 = 14h² × 4

3/28 = h² .......... 1 eqn.

Therefore,

❥ The cost of tiling the floor at the rate of ₹ 10 per m²

❥ Area = L × B

↠ 4h × 3h

↠ 12h²

↠ 12 × 3/28 ....... from equation (1)

↠ 18 / 14 m²

↠ 9/7 m²

❥ Let's find cost now .

❥ Cost = Rate × Area

↠ 10 × 9/7

↠ ₹ 12.85

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

The cost of tiling the floor is ₹ 12.85