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Algebra Level 3

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

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

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

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

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

1 solution

Shauryam Akhoury
Sep 13, 2018

Let the number of goods produced in one hour by one person be $K$ then,

( $p$ People) $*$ ( $p$ days) $*$ ( $p$ hours/day) $*$ ( $K$ objects/hour/people) = $p$ objects

$K=$ $1/(p^2$ )

Then the units of goods produced by $q$ persons working $q$ hours a day for each of $q$ days is

( $q$ People) $*$ ( $q$ days) $*$ ( $q$ hours/day) $*$ ( $K$ objects/hour/people) = $q^3$ $*$ $K$ = $q^3/p^2$ objects

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