Question

The cost of papering the walls of the room 12 m long at the rate of Rs.1.35 per metre square is Rs.340.20 and the cost of matting the floor at the rate of 85 praise per metre square is Rs.91.80. Find the height of the room​

Answer 1

$\sf \: Here, the \: length \: of the \: room \: (L) = 12 \: m$

$\sf \: Let \: breadth \: and \: height \: of \: the \: room \: be \: b \: metre \: and \: h \: metre \: respectively.$

$\sf \: \therefore Area \: of \: four \: walls = 2(2 + b)h$

$\sf \: Since \: cost \: of \: papering \: the \: walls \: per \: m^ {2} \: is \: Rs. \: 1.35$

$\sf \: \therefore Total \: cost \: of \: papering \: walls = [2(12 + b)h] \times 1.35$

$\sf \: According \: to \: question,$

$\sf \implies \: 2(12 + b)h \times (1.35) = 340.20$

$\sf \implies \:2.7 \: h (12 + b) = 340.20$

$\sf \implies \:(12 + b) = \dfrac{340.20}{2.7}$

$\sf \implies \:\:(12 + b) = 126 \: - - - \boxed{1}$

$\sf \: Also, cost \: of \: matting \: the \: floor \: per \: m^{2} \: is \: Rs. \: 0.85$

$\sf \: \therefore Total \: cost \: of \: matting \: the \: floor = 12 \times b \times 0.8$

$\sf \: Total \: cost \: of \: matting \: the \: floor = 10.2 \: b$

$\sf \: According \: to \: question,$

$\sf \implies \: 10.2 \: b = 91.80$

$\sf \implies \: b = \: \dfrac{10.2}{91.80} = 9- - - \boxed{2}$

$\sf \: From \: \boxed{1} \: and \: \boxed{2}, we \: obtained$

$\sf \implies \:(12 + 9) \: h = 126$

$\sf \implies \:21 \: h = 126$

$\sf \implies \:h = \dfrac{126}{21 }$

$\sf \implies \:h =6$

$\underline {\boxed{ \pink{ \sf \: Hence \: the \: height \: of \: the \: room \: is \: 6 \: metre. }}}$