Question

A medical practitioner has created different potencies of a commonly used medicine by dissolving tablets in water and using the resultant solution. Potency 1 solution: When 1 tablet is dissolved in 50 ml, the entire 50 ml is equivalent to one dose. Potency 2 solution: When 2 tablets are dissolved in 50 ml, the entire 50 ml of this solution is equivalent to 2 doses, ... and so on. This way he can give fractions of tablets based on the intensity of infection and the age of the patient. For particular patient, he administers 10 ml of potency 1, 15 ml of potency 2 and 30 ml of potency 4. The dosage administered to the patient is equivalent to

• A. > 2 and \(\leq 3\) tablets
• B. > 3 and \(\leq 3.25\) tablets
• C. > 3.25 and \(\leq 3.5\) tablets
• D. > 3.5 and \(\leq 3.75\) tablets
• E. > 3.75 and \(\leq 4\) tablets

Hint:

- Break down each potency solution into "tablets per ml" first.
- Multiply by the volume consumed to get equivalent tablets.
- Add contributions from all potencies to get total effective dosage.

Answer 1

The Correct Option is B

Step 1: Potency 1 solution.
1 tablet dissolved in 50 ml.
\(\Rightarrow\) 50 ml = 1 tablet.
\(\Rightarrow\) 1 ml = \( \tfrac{1}{50} \) tablet.
\(\Rightarrow\) 10 ml = \( \tfrac{10}{50} = 0.2 \) tablet.
Step 2: Potency 2 solution.
2 tablets dissolved in 50 ml.
\(\Rightarrow\) 50 ml = 2 tablets.
\(\Rightarrow\) 1 ml = \( \tfrac{2}{50} = 0.04 \) tablets.
\(\Rightarrow\) 15 ml = \( 15 \times 0.04 = 0.6 \) tablets.
Step 3: Potency 4 solution.
4 tablets dissolved in 50 ml.
\(\Rightarrow\) 50 ml = 4 tablets.
\(\Rightarrow\) 1 ml = \( \tfrac{4}{50} = 0.08 \) tablets.
\(\Rightarrow\) 30 ml = \( 30 \times 0.08 = 2.4 \) tablets.
Step 4: Total equivalent dosage.
Total = \(0.2 + 0.6 + 2.4 = 3.2\) tablets.
Step 5: Compare with options.
This lies in the range \(> 3\) and \(\leq 3.25\).
\[ \boxed{> 3 \text{and} \leq 3.25 \text{tablets}} \]