Question

The length of a room is two times its breadth and it contains 320 metre cube of air. If the cost of painting its wall at rupees 7.50 per square metre is rupees 1200, find the height of the room.

Answer 1

$\blue{\mathfrak{\underline{\large{Given}}}: } \\ length \: of\: room (l)= 2 \times breadth(b) \\ volume \: of \: air = 320 \: {m}^{3} \\ cost \: of \: painting \: walls \: at \: rupees \: 7.50/ {m}^{2} \\ = 1200 \\ \blue{\mathfrak{\underline{\large{To \: find}}}:} \\ height \: of \: room(h) \\ \blue{\mathfrak{\underline{\large{Finding}}}:} \\ l = 2b - (i) \\ area \: of \: four \: walls = \frac{1200}{7.5} \\ 4 \times l \times b = 160 \\ l \times b = 40 - (ii) \\ volume \: of \: air \: = volume \: of \: room = 320 \: {m}^{3} \\ volume \: of \: room = 320 \\ l \times b \times h = 320 \\ \blue{\mathfrak{\underline{\large{using \: {eq}^{n} \: (ii)}}}:}\\ 40\times h = 320 \\ h = \frac{320}{40} \\ \bf{\boxed{ h = 8 \: m}} \\ \blue{\mathfrak{\large{Height \: of \: room = 8 \: m}}} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$