Question

If p persons working p hours a day for each of p days produce p units of works, then the units of work produced by q persons working q hours a day for each of q days is

• A. $\frac{q^3}{p^2}$
• B. $\frac{q^2}{p^3}$
• C. $\frac{p^2}{q^3}$
• D. $\frac{p^3}{q^2}$

Answer 1

Answer: (A)

$\frac{q^3}{p^2}$

$\because$ Persons working p hours a day in p days produce p units of work
$\therefore$ 1 person working 1 hours a day in 1 day produces
$=\frac{p}{p\times p\times p}$
$\therefore$ q persons working q hours a day in q days produce
$=\frac{p\times q\times q\times q}{p^3}=\frac{q^3}{p^2}$