$\sqrt{960}+9.92\%\text{of}419=?+\frac{1}{5}\times 319$

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

To find the approximate value that will come in place of the question mark (?), let us simplify each term step-by-step using approximation.

The given equation is:

$\sqrt{960}+9.92\%\text{of}419=?+\frac{1}{5}\times 319$

Step 1: Approximate each term in the equation.

1. Approximate $\sqrt{960}$:
Since 960 is very close to 961, and $\sqrt{961}=31$, we can take:
$\sqrt{960}\approx 31$

2. Approximate $9.92\%\text{of}419$:
We can approximate 9.92% to 10%, and 419 to 420.
$10\%\text{of}420=\frac{10}{100}\times 420=42$

3. Approximate $\frac{1}{5}\times 319$:
We can approximate 319 to 320, which is easily divisible by 5.
$\frac{1}{5}\times 320=64$

Step 2: Substitute the approximated values back into the original equation.

$31+42=?+64$

Step 3: Solve for the question mark (?).

$73=?+64$

$?=73-64$

$?=9$

Therefore, the correct answer is 9.