The length and breadth of a hall are in the ratio $4 : 3$ and its height is $5.5$ metres. The cost of decorating its walls (including doors and windows) at $Rs.\ 6.60$ per square metre is $Rs.\ 5082$. Find the length and breadth of the room.

Given:

The length and breadth of a hall are in the ratio $4 : 3$ and its height is $5.5$ metres. The cost of decorating its walls (including doors and windows) at $Rs.\ 6.60$ per square metre is $Rs.\ 5082$.

To do:

We have to find the length and breadth of the room.

Solution:

Ratio in length and breadth of the hall $= 4:3$

Let length $=4x$ and breadth $=3x$

Height of the hall $(h) = 5.5\ m$

Cost of decorating the walls of a room including doors and windows $= Rs.\ 5082$

Rate of decorating $= Rs.\ 6.60$ per $m^2$

This implies,

Area $=\frac{\text { Total cost }}{\text { Rate }}$

$=\frac{5082}{6.60}$

$=\frac{5082 \times 100}{660}$

$=770\ m^2$

Area of four walls $=2 h(l+b)$

$=2 \times 5.5(4 x+3 x)$

This implies,

$11 \times 7 x=770$

$x=\frac{770}{11 \times 7}$

$x=10$

Length of the room $=4x=4 \times 10$

$=40 \mathrm{~m}$

Breadth of the room $=3 x=3 \times 10$

$=30 \mathrm{~m}$

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Updated on: 10-Oct-2022

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