Question

A young child weighing 20 kg was given a drug in the dose 100 mg/kg body weight. The plasma concentration of the drug is 2 mg/dl and the clearance is 200 ml/hr. What is the time required to reach steady state plasma concentration?

• A. 10 hrs
• B. 20 hrs
• C. 30 hrs
• D. 40 hrs

Hint:

Find Vd, then half-life from 0.693 x Vd / CL, then multiply by about 5.5.

Answer 1

The Correct Option is B

Step 1: Begin with the administered amount: multiplying the per-kilogram dose by the child's weight gives $100 \times 20 = 2000$ mg as the total drug given.

Step 2: The apparent distribution space follows from dividing the total amount by the measured plasma level: $V_d = 2000 / 2 = 1000$.

Step 3: Now derive the elimination half-life from the standard relation linking it to volume of distribution and clearance: $t_{1/2} = 0.693 \times V_d / CL = 0.693 \times 1000 / 200 = 3.5$ hours.

Step 4: A drug attains steady state after roughly 5 to 5.5 half-lives; using 5.5, the time is $5.5 \times 3.5 = 19.25$ hours, best matched by the 20-hour option.

\[\boxed{20\ \text{hours}}\]