Question

The cost of papering the four walls of a room at $75$ paise per square metre is Rs. $240$. The height of the room is $5$ metre. Find the length and the breadth of the room, if they are in the ratio $5:3$.

• A. $20$ m and $12$ m
• B. $15$ m and $9$ m
• C. $25$ m and $15$ m
• D. $30$ m and $18$ m

Answer 1

The correct option is A $20$ m and $12$ m

Let the length of the room be $5x$
and breadth of the room be $3x$
Surface area of the four walls $=$ $2(5x\times 5+3x\times 5)$
$=$ $80x{m}^2$ (i)
Cost of papering $1m^2=0.75$Rs.
Total cost of papering $=$ $240$Rs
$\therefore$ surface area of wall $=$ $\frac{1}{0.75}\times 240$
$=$ $320m^2$
Comparing equation (i) and (ii), we get
$80x=320$
$\Rightarrow x=\frac{320}{80}$
$\Rightarrow x=4$ m
$\therefore$ the length of the room be $5\times 4=20$ m
The breadth of the room be $3\times 4=12$ m