Find the approximate value that should replace the question mark (?) in the given expression.

$20.09\%\text{of}?+70.03\%\text{of}699.92=\sqrt{676.09}÷12.97+499.99$

The correct option is 60.

We need to find the approximate value that replaces the question mark (?) in the following expression:

$20.09\%\text{of}?+70.03\%\text{of}699.92=\sqrt{676.09}÷12.97+499.99$

Let us approximate the values in the expression to their nearest integers/convenient values:

• $20.09\%\approx 20\%$
• $70.03\%\approx 70\%$
• $699.92\approx 700$
• $\sqrt{676.09}\approx \sqrt{676}=26$
• $12.97\approx 13$
• $499.99\approx 500$

Substituting these approximate values into the original expression gives:

$20\%\text{of}?+70\%\text{of}700=26÷13+500$

Now, simplify both sides of the equation step-by-step:

Step 1: Calculate the value on the Right-Hand Side (RHS)

$\text{RHS}=(26÷13)+500$

$\text{RHS}=2+500=502$

Step 2: Calculate the known portion of the Left-Hand Side (LHS)

$70\%\text{of}700=\frac{70}{100}\times 700=490$

Step 3: Equate LHS and RHS to solve for (?)

$20\%\text{of}?+490=502$

$20\%\text{of}?=502-490$

$20\%\text{of}?=12$

$\frac{20}{100}\times ?=12$

$\frac{1}{5}\times ?=12$

$?=12\times 5=60$

Thus, the approximate value that should replace the question mark (?) is 60.