Question-17

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item.

In selling these two items, the person made a total of

• 1% profit
• 2% profit
• 1% loss
• 2% loss

NoteAnswer

• 1% profit
• 2% profit
• 1% loss
• 2% loss

NoteSoluton

Let \(\displaystyle x\) and \(\displaystyle y\) be the cost prices of the two items. With the given information, their selling prices are \(\displaystyle 1.1x\) and \(\displaystyle 0.9y\) respectively. Since they are equal, let:

\[\begin{equation*} 1.1x=0.9y=p \end{equation*}\]

Now, the profit percentage on selling both together is:

\[ \begin{aligned} \frac{( 1.1x+0.9y) -( x+y)}{x+y} \times 100 & =\frac{0.1x-0.1y}{x+y} \times 100\\\\ & =\frac{\frac{p}{1.1} -\frac{p}{0.9}}{\frac{p}{1.1} +\frac{p}{0.9}} \times 10\\\\ & =-1 \end{aligned} \]

Therefore, there is a loss of \(\displaystyle 1\%\).