The normal dosage of a particular medicine is $t$ tablets per day for each patient. A hospital's current supply of these tablets will last $p$ patients for $d$ days. If the recommended dosage increases by 20\% and the number of patients decreases by one-third, then for how many days will the hospital's supply last?
(a)$\frac{5 d}{4}$
(b)$\frac{4 d}{5}$
(c)$\frac{4 p t}{5}$
(d)Cannot be determined
Answer
Answer (as printed): A
Explanation
New dosage $= 120\%$ of $t = \frac{6}{5}t$. Number of patients decreases by one-third $\Rightarrow$ new number of patients $= \frac{2}{3}p$. Let the required number of days be $x$. More dosage, Less days (Indirect Proportion). Less patients, More days (Indirect Proportion). Dosage $\frac{6}{5}t : t$, Patients $p : \frac{2}{3}p$ :: $d:x$. $\therefore \frac{6}{5}t \times p \times x = t \times \frac{2}{3}p \times d \Leftrightarrow x = \frac{5}{6} \times \frac{3}{2} \times d = \frac{5d}{4}$.
Explanation as extracted from the printed page; notation may be imperfect.