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 answer is 32 m.

Let us define the variables. Let the breadth of the rectangular field be b metres. Since the length is thrice the breadth, the length is 3b metres.

Step 1: Find the total length of fencing (Perimeter)

Fencing covers the perimeter of the field. The rate is Rs. 7.5 per metre, and the total cost is Rs. 960. So:

\text{Perimeter}=\frac{\text{Total Cost}}{\text{Rate per metre}}=\frac{960}{7.5}=128\text{m}

Step 2: Apply the perimeter formula

The perimeter of a rectangle is 2(l+b). Substituting l=3b:

2(3b+b)=128

2\left(4b\right)=128

8b=128

b=\frac{128}{8}=16\text{m}

Step 3: Find the Length

l=3b=3\times 16=48\text{m}

Step 4: Calculate the Difference between Length and Breadth

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

Therefore, the difference between the length and the breadth of the field is 32 m.