Question

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.

Answer 1

Cost of preparing walls of a room$=Rs340.20$

$Rate=Rs1.35per{m}^2$

$\therefore \text{Area of walls}=\frac{340.20}{1.35}=\frac{34020}{135}{m}^2$

$\text{Length of wall}\left(l\right)=12m$

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

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

$=\frac{126}{l+b}...\left(i\right)$

$\text{Cost of making the floor}=Rs91.80$

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

$\therefore \text{Area of floor}=\frac{9180}{85}=108m^2$

Length (l) = 12 m

$\therefore Breadth=\frac{Area}{Length}=\frac{108}{12}=9m$

From (i), $h=\frac{126}{l+b}=\frac{126}{12+9}=\frac{126}{21}=6m$

$\therefore \text{Height of room}=6m$