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

$420.25+580.12-149.98\%\text{of}640.18=?-110.05\times \sqrt{35.91}$

The correct answer is 700.

To find the approximate value that comes in place of the question mark (?), we round off the values in the equation to their nearest whole numbers for easier calculation:

$420.25\approx 420$
$580.12\approx 580$
$149.98\%\approx 150\%$
$640.18\approx 640$
$110.05\approx 110$
$\sqrt{35.91}\approx \sqrt{36}=6$

Now, substitute these approximate values into the given equation:

$420+580-150\%\text{of}640=?-110\times 6$

Step 1: Calculate $150\%\text{of}640$:

$150\%\text{of}640=\frac{150}{100}\times 640=1.5\times 640=960$

Step 2: Calculate the product on the right-hand side:

$110\times 6=660$

Step 3: Substitute these values back into the equation:

$420+580-960=?-660$

$1000-960=?-660$

$40=?-660$

Step 4: Solve for $?$:

$?=40+660=700$

Hence, the approximate value that should come in place of the question mark (?) is 700.