the perimeter of a rectangle is 240 cm . if its lenghtis increased by 10 %n its breadth is increased by 20%,we get the same perimeter > find the length n breadth of the rectangle ??

Suppose l and b be the length and breadth of the rectangle respectively.
So perimeter of rectangle = $2\left(l+b\right) = 240 \mathrm{cm}$
$\Rightarrow \left(l+b\right) = 120......\left(\mathrm{i}\right)$
when length is decreased by 10%, then new length = $l-l\times \frac{10}{100} = \frac{9l}{10}$
And when breadth is increased by 20%, then new breadth = $b+b\times \frac{20}{100} = \frac{6b}{5}$
So, according to the question we have;
Perimeter = $2\left[\frac{9l}{10}+\frac{6b}{5}\right] = 240 \mathrm{cm}$
$$\begin{gathered} \Rightarrow 2\left[\frac{9l+12b}{10}\right] = 240 \\ \Rightarrow 9l+12b = \frac{240\times 10}{2} \\ \Rightarrow 3\left(3l+4b\right) = 1200 \\ \Rightarrow 3l+4b = 400 ......\left(\mathrm{ii}\right) \end{gathered}$$
Now multiplying (i) by 3 and subtract (ii) from (i) we get;
$$\begin{gathered} 3l+3b-3l-4b = 360-400 \\ \Rightarrow -b = -40 \\ \Rightarrow b = 40 \end{gathered}$$
Putting b = 40 in (i) we get;
$l = 120-40 = 80$
Therefore length and breadth of rectangle are 80 cm and 40 cm respectively.