What approximate value should come in place of question mark (?) in the following equation.

$111.99\%\text{of}?+249.92\%\text{of}191.93={\left(27.98\right)}^2-\sqrt[3]{511.99}$

The correct option is 264.

To find the approximate value of the question mark (?), we can round each decimal number in the given equation to its nearest convenient whole number:

• 111.99% ≈ 112%

• 249.92% ≈ 250%

• 191.93 ≈ 192

• 27.98 ≈ 28

• 511.99 ≈ 512

Now, let us rewrite the equation using these approximate values:

$112\%\text{of}?+250\%\text{of}192={\left(28\right)}^2-\sqrt[3]{512}$

Step 1: Simplify the right-hand side (RHS) of the equation.

Calculate 28²:

${\left(28\right)}^2=784$

Calculate the cube root of 512:

$\sqrt[3]{512}=8$

Subtract the cube root value from the squared value:

$\text{RHS}=784-8=776$

Step 2: Simplify the known part of the left-hand side (LHS).

Calculate 250% of 192:

$250\%\text{of}192=\frac{250}{100}\times 192=2.5\times 192=480$

Step 3: Substitute the calculated values back into the equation.

$112\%\text{of}?+480=776$

Subtract 480 from both sides:

$112\%\text{of}?=776-480$

$112\%\text{of}?=296$

Step 4: Solve for question mark (?).

$\frac{112}{100}\times ?=296$

$?=\frac{296\times 100}{112}$

$?=\frac{29600}{112}\approx 264.28$

Thus, the approximate value of (?) is 264.