The length of rectangular field is thrice its breadth. If Rs. 960 is required to fencing the field at the rate Rs 7.5 per sq. m, then what would be the difference between the length and breadth of the field?

The correct option is 32 m.

Step-by-step Derivation:

Step 1: Express the dimensions of the rectangular field.
Let the breadth of the rectangular field be $b$ meters.
Since the length is thrice its breadth, the length ($l$) can be expressed as:

$l=3b$

Step 2: Relate the dimensions to the perimeter.
Fencing is always done along the boundary (perimeter) of the rectangular field. Note that the rate of Rs. 7.5 per sq. m is a typographical representation of the rate per meter of the perimeter.
The perimeter ($P$) of a rectangle is calculated as:

$P=2(l+b)$
Substituting $l=3b$ into the equation:

$P=2(3b+b)=2\left(4b\right)=8b$

Step 3: Calculate the breadth of the field using the cost of fencing.
The total cost of fencing is the product of the perimeter and the rate per meter:

$\text{Total Cost}=\text{Perimeter}\times \text{Rate}$
Substitute the given values (Total Cost = Rs. 960, Rate = Rs. 7.5 per meter):

$960=8b\times 7.5$
$960=60b$
Divide both sides by 60 to find $b$:

$b=\frac{960}{60}=16\text{m}$

Step 4: Find the difference between the length and breadth.
Now, find the length ($l$) of the field:

$l=3\times 16=48\text{m}$
Finally, calculate the difference between the length and breadth:

$\text{Difference}=l-b=48-16=32\text{m}$