What approximate value will come in place of question mark (?) in the following questions (You are not expected to calculate the exact value).

$\frac{32.08\%\text{ of }599}{1.99}÷\frac{1}{4}={?}^2-16$

Correct Answer: 20 (Option 20)

Step-by-step Explanation:

We are given the following approximation expression:

$\frac{32.08\%\text{ of }599}{1.99}÷\frac{1}{4}={?}^2-16$

Step 1: Approximate the numbers to their nearest integers for quick calculation.

• 32.08% ≈ 32%

• 599 ≈ 600

• 1.99 ≈ 2

Step 2: Simplify the numerator of the left side.

$32\%\text{ of }600=\frac{32}{100}\times 600=32\times 6=192$

Step 3: Divide by 1.99 (approximated to 2).

$\frac{192}{2}=96$

Step 4: Perform the division by 1/4.

Dividing by a fraction is equivalent to multiplying by its reciprocal:

$96÷\frac{1}{4}=96\times 4=384$

Step 5: Solve for the unknown variable (?).

Now substitute 384 back into the equation:

$384={?}^2-16$

Add 16 to both sides:

${?}^2=384+16$

${?}^2=400$

Take the square root of both sides:

$?=\sqrt{400}=20$

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