What approximate value will come in place of question mark (?) in the…

Concept

In an approximation problem, round every number to the nearest convenient figure, evaluate the expression in the rounded form, and read off the option closest to the result. Two rules drive this item: a percentage means (rate/100) × base, and dividing by a fraction equals multiplying by its reciprocal, so ÷ (1/4) = × 4. Once the left side is a number N and the equation reads N = ?2 − 16, solve for ? as the square root of (N + 16).

Application

1. Round the values: 32.08% ≈ 32%, 599 ≈ 600, 1.99 ≈ 2.

2. Percentage: 32% of 600 = (32/100) × 600 = 192.

3. Divide by 1.99 ≈ 2: 192 ÷ 2 = 96.

4. Divide by the fraction: 96 ÷ (1/4) = 96 × 4 = 384. This is the value of the whole left-hand side, N.

5. Set up the equation: 384 = ?2 − 16, so ?2 = 384 + 16 = 400.

6. Take the square root: ? = √400 = 20.

Cross-check

Using the unrounded numbers: 32.08% of 599 = 192.16; ÷ 1.99 = 96.56; × 4 = 386.25; + 16 = 402.25; √402.25 ≈ 20.06. This rounds cleanly to 20, confirming the rounded computation. The value 20 is the result.