A rectangular plot of perimeter 60 m is to be fenced. Fencing costs Rs 40 per metre along each length and Rs 30 per metre along each breadth, and the whole fence costs Rs 2160. Find the length of the plot.

Let the length be $x$ m and the breadth $y$ m. The perimeter gives $2(x+y)=60$, so $x+y=30$. The cost covers two lengths and two breadths: $2(40x)+2(30y)=2160$, that is $80x+60y=2160$, or $4x+3y=108$. Substituting $y=30-x:4x+90-3x=108$, so $x=18$ and $y=12$. Check: $2(18+12)=60$ and 1440 + 720 = 2160. 12 m is the breadth; 30 m is half the perimeter, that is length plus breadth; 15 m assumes the plot is a square, which would cost 2400 + 900 = Rs 2100, not Rs 2160.