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

$419.99\%\text{of}75.02=69.92\%\text{ of}\mathrm{ 750.02}-?\%\text{of}1049.97$

The correct answer is 20 (Option 3).

To solve this simplification problem, we first round off the given numbers to their nearest integers to find the approximate value of the question mark (?):

• 419.99% ≈ 420%

• 75.02 ≈ 75

• 69.92% ≈ 70%

• 750.02 ≈ 750

• 1049.97 ≈ 1050

Now, let us rewrite the given equation with these approximate values:

$420\%\text{of}75=70\%\text{of}750-?\%\text{of}1050$

Step 1: Calculate the value of the left-hand side (LHS).

$420\%\text{of}75=\frac{420}{100}\times 75=4.2\times 75=315$

Step 2: Calculate the value of the first term on the right-hand side (RHS).

$70\%\text{of}750=\frac{70}{100}\times 750=7\times 75=525$

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

$315=525-?\%\text{of}1050$

Step 4: Rearrange the equation to isolate the term containing "?".

$?\%\text{of}1050=525-315$

$?\%\text{of}1050=210$

Step 5: Solve for "?".

$\frac{?}{100}\times 1050=210$

$?=\frac{210\times 100}{1050}$

$?=\frac{21000}{1050}=20$

Hence, the approximate value that comes in place of question mark (?) is 20.