The cost of preparing the walls of a room $12\ m$ long at the rate of $Rs.\ 1.35$ per square metre is $Rs.\ 340.20$ and the cost of matting the floor at $85$ paise per square metre is $Rs.\ 91.80$. Find the height of the room.

Given:

The cost of preparing the walls of a room $12\ m$ long at the rate of $Rs.\ 1.35$ per square metre is $Rs.\ 340.20$ and the cost of matting the floor at $85$ paise per square metre is $Rs.\ 91.80$.

To do:

We have to find the height of the room.

Solution:

Cost of preparing the walls of the room $= Rs.\ 340.20$

Rate $=Rs.\ 1.35$ per $\mathrm{m}^{2}$
Therefore,

Area of walls $=\frac{340.20}{1.35}$

$=\frac{34020}{135} \mathrm{~m}^{2}$

Length of the wall $(l)=12 \mathrm{~m}$

Height of the walls $(h)=\frac{\text { Area }}{2(\text { Length }+\text { Breadth })}$

$=\frac{34020}{135 \times 2(l+b)}$

$=\frac{126}{l \times b}$

Cost of matting the floor $=Rs.\ 91.80$

Rate $=85$ paise per sq. $\mathrm{m}$

Area of floor $=\frac{9180}{85}$

$=108 \mathrm{~m}^{2}$

Length $(l)=12 \mathrm{~m}$

Breadth $=\frac{\text { Area }}{\text { Length }}$

$=\frac{108}{12}$

$=9 \mathrm{~m}$

This implies,

$h=\frac{126}{l+b}$

$=\frac{126}{12+9}$

$=\frac{126}{21}$

$=6 \mathrm{~m}$

The height of the room is $6 \mathrm{~m}$.

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Updated on: 10-Oct-2022

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