Question

length of a room is two times its height and its breadth is 1/3 times its height.the cost of white washing the walls at the rate of Rs.1.60per metre square is rs 179.20. find the cost of tilling the floor at the rate rs 6.75per metre square​

Answer 1

let the height of the room=x

length of the room = 2x

breadth________=x/3

Therfore the cost of white washing= 6.75 X 179.20

= 1120

Answer 2

Answer:

Let the height of the classroom be h metres. Then,

• Length = 2h

• Breadth = $\sf\dfrac{3}{2}$ h metres.

$\\ \therefore \sf \small Area \: of \: four \: walls = 2 \times height \: (length + breadth) \\ \\ \\ \implies \sf \bigg \{ 2 \times h \times \bigg(2h + \frac{3}{2} h \bigg) \bigg \} \: {m}^{2} \\ \\ \\ \implies \sf \bigg \{2 \times h \times \bigg( \frac{4h + 3h}{2} \bigg) \bigg \} \: {m}^{2} \\ \\ \\ \implies \sf \bigg \{2 \times h \times \frac{7h}{2} \bigg \} \: {m}^{2} \\ \\ \\ \implies \sf \blue{7 {h}^{2} \: {m}^{2} }$

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We have,

• Cost of white Washing of 1 m² = Rs 1.60

$\therefore$ Cost of white Washing of the four walls -

= Rs (1.60 × 7 h²) = Rs 11.20 h²

But, the cost of white Washing is given in the question -

• Rs 179.20

$\\ \therefore \qquad \sf 11.20 \: {h}^{2} = 179.20 \\ \\ \\ \implies \sf {h}^{2} = \frac{179.20}{11.20} = 16 \\ \\ \\ \implies \sf {h}^{2} = {4}^{2} \\ \\ \\ \implies \sf \green{h = 4}$

____________________

$\therefore \qquad \sf \small Length \: \: of \: \: the \: \: classroom \: \: : - \\ \\ \\ \rightarrow \sf(2 \times 4) \: m = 8m \\ \\ \\ \therefore\qquad \small \sf \: Breadth \: \: of \: \: the \: \: classroom \: \: : - \\ \\ \\ \rightarrow \: \sf \bigg( \frac{3}{2} \times 4 \bigg) \: m = 6 \: m$

$\therfore$ Area of floor of the room = ( 8 × 6 ) m² = 48 m²

We have,

• Cost of titling of 1 m² of the floor = Rs 6.75

$\therefore$ Cost of titling the floor = Rs ( 6.75 × 48 ) = Rs 324