Question

please answer this question ​

Answer 1

To find:

The cost of cementing the floor at the rate of ₹ 6.75 per sq m

Step-by-step explanation:

Let the height of the room be $h$ m

Then length is $2h$ m

and breadth is $1\dfrac{1}{2}h$ m = $\dfrac{3}{2}h$ m

There are two walls on the length and two walls on the breadth. Thus the area of the four walls

$=2\times 2h\times h+2\times \dfrac{3}{2}h\times h$ sq m

$=7h^{2}$ sq m

The cost of distempering the walls at the rate of ₹ 14.85 per sq m is ₹ 1663.20

So, the area of the walls

$=\dfrac{total\:cost}{per\:m\:cost}$

$=\dfrac{1663.20}{14.85}$ sq m

$=112$ sq m

According to the question, (numerically)

$\quad 7h^{2}=112$

$\Rightarrow h^{2}=16$

$\Rightarrow h=4$ (negative value is neglected)

Then the height of the walls is $4$ m

Thus length of the room is $2\times 4$ m = $8$ m and the breadth of the room is $\dfrac{3}{2}\times 4$ m = $6$ m

Hence the area of the floor

= length × breadth

$=8\times 6$ sq m

$=48$ sq m

Therefore the cost of cementing the floor at the rate of ₹ 6.75 per sq m is ₹ $6.75\times 48$ = ₹ $324$

Answer: Required cost is ₹324.