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Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A. A profit of 10
B. A profit of 8
C. A loss of 8
D. A loss of 10
E. Neither a profit nor a loss

(Common) Assumption: although not explicitly mentioned, we are dealing with profit of 20% over the cost on the corresponding sale. The same for the loss.

\[?\,\,\,:\,\,\,{\text{profit/loss}}\,\,\left( \$ \right)\]
\[1{\text{st}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 + \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{6}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{profit}} = \frac{1}{6}\left( {96} \right) = \underleftrightarrow {\frac{{60 + 36}}{6}} = 16\,\,\,\left( \$ \right)\]
\[2{\text{nd}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 - \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{4}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{loss}} = \frac{1}{4}\left( {96} \right) = \underleftrightarrow {\frac{{80 + 16}}{4}} = 24\,\,\left( \$ \right)\]
\[?\,\, = \,\,\,16 + \left( { - 24} \right) = - 8\,\,\left( \$ \right)\]

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

Regards,
Fabio.