Problem Solving

Source: e-GMAT

A newly-opened retail store made $400 profit on the initial expenditure of $25,000 and then made $1,200 profit on the next $80,000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25,000 expenditure to the next $80,000 expenditure?

A. 6.67% decrease
B. 6.25% decrease
C. 0
D. 6.25% increase
E. 6.67% increase

The OA is B.

BTGmoderatorLU wrote:Source: e-GMAT

A newly-opened retail store made $400 profit on the initial expenditure of $25,000 and then made $1,200 profit on the next $80,000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25,000 expenditure to the next $80,000 expenditure?

A. 6.67% decrease
B. 6.25% decrease
C. 0
D. 6.25% increase
E. 6.67% increase

\[\left. \begin{gathered}
{\text{I}}{\text{.}}\,\,\,\frac{{400}}{{25000}} = \frac{2}{{125}} \hfill \\
{\text{II}}{\text{.}}\,\,\,\frac{{1200}}{{80000}} = \frac{3}{{200}} \hfill \\
\end{gathered} \right\}\,\,\,\,?\,\, = \Delta \% \left( {\,{\text{I}}\,\,\, \to \,\,\,{\text{II}}\,} \right)\]
\[? = \frac{{\frac{3}{{200}} - \frac{2}{{125}}}}{{\frac{2}{{125}}}} = \frac{{125}}{2}\left( {\frac{{3 \cdot \boxed5}}{{8 \cdot 25 \cdot \boxed5}} - \frac{{2 \cdot \boxed8}}{{5 \cdot 25 \cdot \boxed8}}} \right) = \frac{{5 \cdot 25}}{2}\left( { - \frac{1}{{5 \cdot 25 \cdot 8}}} \right) = - \frac{1}{{16}}\]
\[? = - \frac{1}{4}\left( {\frac{1}{4}} \right) = - \frac{1}{4}\left( {25\% } \right) = - 6\frac{1}{4}\% \,\,\,\,\, \Rightarrow \,\,\,\,\left( B \right)\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.