Questions: A salesman sold two notebooks at 12 riyals each. His profit on one was 20% and the loss on the other was 20%. Then on the whole, he: (A) Lost 1 riyal. (B) Gained 1 riyal. (C) Neither gained nor lost. (D) Lost 2 riyals. (E) Gained 2 riyals.

Solution Steps

To determine the overall profit or loss, we need to calculate the cost price of each notebook and then compare it to the selling price.

1. For the notebook sold at a 20% profit:

   • Let the cost price be \( CP_1 \).
   • Selling price \( SP_1 = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \).
   • Given \( SP_1 = 12 \) riyals, we can solve for \( CP_1 \).

2. For the notebook sold at a 20% loss:

   • Let the cost price be \( CP_2 \).
   • Selling price \( SP_2 = CP_2 - 0.2 \times CP_2 = 0.8 \times CP_2 \).
   • Given \( SP_2 = 12 \) riyals, we can solve for \( CP_2 \).

3. Calculate the total cost price and total selling price, then find the difference to determine the overall profit or loss.

For the notebook sold at a 20% profit, let the cost price be \( CP_1 \). The selling price is given by:

\[ SP_1 = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \]

Given \( SP_1 = 12 \) riyals, we can solve for \( CP_1 \):

\[ CP_1 = \frac{SP_1}{1.2} = \frac{12}{1.2} = 10 \text{ riyals} \]

For the notebook sold at a 20% loss, let the cost price be \( CP_2 \). The selling price is given by:

\[ SP_2 = CP_2 - 0.2 \times CP_2 = 0.8 \times CP_2 \]

Given \( SP_2 = 12 \) riyals, we can solve for \( CP_2 \):

\[ CP_2 = \frac{SP_2}{0.8} = \frac{12}{0.8} = 15 \text{ riyals} \]

Now, we can calculate the total cost price and total selling price:

\[ \text{Total Cost Price} = CP_1 + CP_2 = 10 + 15 = 25 \text{ riyals} \]

\[ \text{Total Selling Price} = SP_1 + SP_2 = 12 + 12 = 24 \text{ riyals} \]

The overall result can be calculated as:

\[ \text{Overall Result} = \text{Total Selling Price} - \text{Total Cost Price} = 24 - 25 = -1 \text{ riyal} \]

This indicates a loss of 1 riyal.

Final Answer