Question

The length and breadth of a rectangular field are in the ratio $5:3$. If the cost of cultivating the field at $25$ paise per square metre is Rs. $6000$, find the perimeter of the field.

• A. $700$ m
• B. $160$ m
• C. $640$ m
• D. $560$ m

Answer 1

Answer: (C)

$640$ m

Let length $=5x$ and breadth $=3x$
$\therefore$ Area $=$ length $\times$ breadth
$=5x\times 3x=15x^2$
Cost of cultivating $1$ square meter $=25$ paise
$\therefore$ Cost of cultivating $15x^2$ square meter $=25\times 15x^2=375x^2$ paise$=$ Rs. $\frac{375}{100}{x}^2$
Given, Rs. $\frac{375}{100}{x}^2=$ Rs. $6000$
$\Rightarrow x^2=\frac{6000\times 100}{375}$
$\Rightarrow x^2=1600$
$\Rightarrow x=40$
$\therefore$ length $=5\times 40=200$ m
and breadth $=3\times 40=120$ m
Since, perimeter $=2($ length $+$ breadth$)$
$=2(200+120)$
$=2\left(320\right)=640$ m
hence, option C is correct.