Question

How many minutes of exposure to the sun in a day would be enough to ensure that the body receives enough Vitamin D, given that the body requires 40 units of Vitamin D every day and that 30 units of Beta rays generate one unit of Vitamin D?

• A. \(5 \tfrac{1}{3}\)
• B. \(5 \tfrac{2}{3}\)
• C. \(6 \tfrac{1}{3}\)
• D. \(6 \tfrac{2}{3}\)

Hint:

Map the chain carefully: \(\text{Vit-D need} \Rightarrow \text{Beta units needed} \Rightarrow \text{time}\). Keep track of units at each step to avoid mistakes.

Answer 1

The Correct Option is D

Step 1: Convert Vitamin D need to Beta-unit need. 
Each 1 unit of Vitamin D needs 30 Beta units. 
Daily need \(= 40\) Vit-D units \(\Rightarrow 40 \times 30 = 1200\) Beta units. 

Step 2: Determine Beta units received per minute. 
From the pie chart, Beta \(= 5\%\) of \(3600 = 180\) units/min. 

Step 3: Compute time (minutes). 
Time \(= \dfrac{\text{required Beta units}}{\text{Beta units per minute}} = \dfrac{1200}{180} = \dfrac{120}{18} = \dfrac{20}{3} = 6.\overline{6}\) minutes. 
In mixed form: \(6 \tfrac{2}{3}\) minutes. 

Step 4: Conclude. 
Required exposure \(= \boxed{6 \tfrac{2}{3}\ \text{minutes}}\).