Question

height of a room is half its length and its breadth is 3 / 2 of its height . if the cost of the painting its four walls the rate of rupees 1.75 per metre square is rupees 196 then find the cost of filing the floor of the room @ rupees 8.50 per metre square.

Answer 1

SOLUTION

GIVEN

• Height of a room is half its length

• Its breadth is 3/2 of its height

• The cost of the painting its four walls the rate of Rs 1.75 per metre square is Rs 196

TO DETERMINE

The cost of filing the floor of the room at the rate of Rs 8.50 per metre square.

EVALUATION

Let the length of the room = 4a metre

So the height of room

$= \displaystyle \sf{ \frac{1}{2} \times 4a \: \: metre}$

$= \displaystyle \sf{2a \: \: metre}$

Breadth of the room

$= \displaystyle \sf{ \frac{3}{2} \times 2a \: \: metre}$

$= \displaystyle \sf{ 3a \: \: metre}$

Hence the area of the four walls

$= \displaystyle \sf{ 2 \times (4a + 3a) \times 2a \: \: \: sq\: metre}$

$= \displaystyle \sf{ 2 \times 7a \times 2a \: \: \: sq\: metre}$

$= \displaystyle \sf{ 28 {a}^{2} \: \: \: sq\: metre}$

So the cost of the painting its four walls the rate of Rs 1.75 per metre square is

$= \displaystyle \sf{ 28 {a}^{2} \: \times 1.75 \: \: }$

So by the given condition

$\displaystyle \sf{ 28 {a}^{2} \: \times 1.75 \: \: = 196 }$

$\displaystyle \sf{ \implies \: 28 {a}^{2} \: = \frac{196}{1.75} }$

$\displaystyle \sf{ \implies \: 28 {a}^{2} \: = \frac{196}{1.75} }$

$\displaystyle \sf{ \implies \: 28 {a}^{2} \: = 112 }$

$\displaystyle \sf{ \implies \: {a}^{2} \: = 4 }$

$\displaystyle \sf{ \implies \: a = 2 }$

∴ Length of the room = ( 4 × 2 ) = 8 metre

Height of the room = ( 2 × 2 ) = 4 metre

Breadth of the room = ( 3 × 2 ) = 6 metre

∴ Area of the floor

= ( 8 × 6 ) sq metre

= 48 sq metre

Hence the cost of filing the floor of the room at the rate of Rs 8.50 per metre square

= Rs ( 48 × 8.50 )

= Rs 408

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If the carriage of 810 kg, for 70km cost Rs.45, what will be the cost of 840kg for a distance of 63 km at the half of the former rate

https://brainly.in/question/12636102

2. A scooter is travelling at uniform speed of 80 km/hr. How much distance it will cover in 24 min.?

https://brainly.in/question/31137065

Answer 2

Step-by-step explanation:

Given height of a room is half its length and its breadth is 3 / 2 of its height . if the cost of the painting its four walls the rate of rupees 1.75 per metre square is rupees 196 then find the cost of filing the floor of the room @ rupees 8.50 per metre square.

• Let the height of the room be h
• So h = ½ of length
• So length = 2h
• Breadth = 3/2 of h  
•               = 1.5 h
• Now Area of four walls = 196 / 1.75
•                                         = 112
• So 2 height (length + breadth) = 112
•      2h (2h + 1.5 h) = 112
•      2h x 3.5 h = 112
•          7 h^2 = 112
•          h^2 = 112 / 7
•        h^2 = 16
•       Or h = 4
• Now height h = 4 m
•  length = 2h
•             = 2 x 4
•             = 8 m
•  breadth = 1.5 h
•               = 1.5 x 4
•                = 6 m
• Area of the floor = length x breadth
•                           = 8 x 6
•                           = 48 sq m
• Cost of tiling the floor of the room per sq m = Rs 8.50
• Therefore cost of tiling 48 sq m = 48 x 8.50
•                                                    = Rs 408

Reference link will be

https://brainly.in/question/2623831