Find the value of [{(82 + 48 ÷ 8 × 3) + 5 × 6 } – 7.5 × 2].

The correct option is 115.

To evaluate the given mathematical expression, we follow the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), solving operations from the innermost brackets outward.

The given expression is:

$\left[\{\left(82+48÷8\times 3\right)+5\times 6\right\}-7.5\times 2]$

Step 1: Simplify the innermost parenthetical expression $\left(82+48÷8\times 3\right)$

First, perform the division operation inside the parentheses:

$48÷8=6$

Next, perform the multiplication operation:

$6\times 3=18$

Now, perform the addition inside the parentheses:

$82+18=100$

Step 2: Simplify inside the curly braces $\left\{100+5\times 6\right\}$

First, perform the multiplication operation inside the curly braces:

$5\times 6=30$

Now, perform the addition:

$100+30=130$

Step 3: Simplify inside the square brackets $\left[130-7.5\times 2\right]$

First, perform the multiplication operation:

$7.5\times 2=15$

Now, perform the final subtraction:

$130-15=115$

Thus, the final value of the given expression is 115.