$380.380+619.99-190.011\%\text{of}820.21=?-120.21\times \sqrt{24.95}$

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

To find the approximate value, we can round off the numbers in the given expression to their nearest convenient integers:

$380.380\approx 380$
$619.99\approx 620$
$190.011\%\approx 190\%$
$820.21\approx 820$
$120.21\approx 120$
$\sqrt{24.95}\approx \sqrt{25}=5$

Now, let's substitute these approximate values back into the original equation:

$380+620-(190\%\text{of}820)=?-120\times 5$

Step 1: Simplify the addition on the left-hand side:

$380+620=1000$

Step 2: Calculate the percentage value:

$190\%\text{of}820=\frac{190}{100}$

Step 3: Simplify the multiplication on the right-hand side:

$120\times 5=600$

Step 4: Rewrite the equation with these values and solve for the unknown (?):

$1000-1558=?-600$
$-558=?-600$
$?=600-558$
$?=42$

Therefore, the approximate value that should come in place of the question mark is 42.