Question - Profit Calculation from Sale of Articles

The image shows a handwritten question about profit calculation.

Let's denote:

\( CP \) = Cost Price

\( SP \) = Selling Price

Given that the seller sells one article for \( \$6000 \) and a loss \( SP = CP - \frac{CP}{7} \).

We then express \( SP \) in terms of \( CP \):

\( SP = CP - \frac{CP}{7} \)

\( SP = \frac{6CP}{7} \)

Now, if the seller sells another article for \( \$7000 \) with a profit of \( SP = CP + \frac{CP}{7} \),

We express this \( SP \) in terms of \( CP \):

\( SP = CP + \frac{CP}{7} \)

\( SP = \frac{8CP}{7} \)

Now we have two equations:

1) \( \frac{6CP}{7} = 6000 \)

2) \( \frac{8CP}{7} = 7000 \)

We can now solve for \( CP \) from either equation, but equation 1) is simpler:

\( CP = \frac{6000 \times 7}{6} \)

\( CP = 7000 \times \frac{7}{6} \)

\( CP = \$7000 \)

Now, find the total profit when he sells both articles:

The profit from selling the second item is \( \$7000 \) with a profit of \( \frac{CP}{7} \):

\( Profit = \frac{CP}{7} \)

\( Profit = \frac{7000}{7} \)

\( Profit = \$1000 \)

Since he sells the first item at a loss of \( \frac{CP}{7} \), which is \( \$1000 \), and the second one at a profit of \( \$1000 \), the total profit is:

\( Total\,Profit = Profit\,from\,second\,item - Loss\,from\,first\,item \)

\( Total\,Profit = \$1000 - \$1000 \)

\( Total\,Profit = \$0 \)

Therefore, the seller neither makes a profit nor incurs a loss overall.