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.

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Solution

## $\mathrm{The}\mathrm{cost}\mathrm{of}\mathrm{preparing}4\mathrm{walls}\mathrm{of}\mathrm{a}\mathrm{room}\mathrm{whose}\mathrm{length}\mathrm{is}12\mathrm{m}\mathrm{is}\mathrm{Rs}340.20\mathrm{at}\mathrm{a}\mathrm{rate}\mathrm{of}\mathrm{Rs}1.35/{\mathrm{m}}^{2}.\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{four}\mathrm{walls}\mathrm{of}\mathrm{the}\mathrm{room}=\frac{\mathrm{total}\mathrm{cost}}{\mathrm{rate}}=\frac{\mathrm{Rs}340.20}{\mathrm{Rs}1.35}=252{\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{Also},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{matting}\mathrm{the}\mathrm{floor}\mathrm{at}85\mathrm{paise}/{\mathrm{m}}^{2}\mathrm{is}\mathrm{Rs}91.80.\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{floor}=\frac{\mathrm{total}\mathrm{cost}}{\mathrm{rate}}=\frac{\mathrm{Rs}91.80}{\mathrm{Rs}0.85}=108{\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{room}=\frac{\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{floor}}{\mathrm{length}}\mathrm{=}\frac{108}{12}=9\mathrm{m}\phantom{\rule{0ex}{0ex}}\mathrm{Suppose}\mathrm{that}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{room}\mathrm{is}\mathrm{h}\mathrm{m}. \mathrm{Then},\mathrm{we}\mathrm{have}:\phantom{\rule{0ex}{0ex}}\mathrm{Area}\mathrm{of}\mathrm{four}\mathrm{walls}=2×\left(\mathrm{length}×\mathrm{height}+\mathrm{breadth}×\mathrm{height}\right)\phantom{\rule{0ex}{0ex}}⇒252=2×\left(12×\mathrm{h}+9×\mathrm{h}\right)\phantom{\rule{0ex}{0ex}}⇒252=2×\left(21\mathrm{h}\right)\phantom{\rule{0ex}{0ex}}⇒21\mathrm{h}=\frac{252}{2}=126\phantom{\rule{0ex}{0ex}}⇒\mathrm{h}=\frac{126}{21}=6\mathrm{m}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{The}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{room}\mathrm{is}6\mathrm{m}.$

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