A shopkeeper bought two units of an article at the same price. He sold one unit at a profit of 30%. If on selling the second unit, he incurred a loss which was one-third of the profit earned on the first unit, what was his overall profit percent ?

Let cost price of each unit = Rs. $$100x$$

=> C.P. of both units = $$2 \times 100x = 200x$$

Profit % on 1st unit = 30%

=> S.P. of one unit = $$\frac{130}{100} \times 100x = 130x$$

=> Profit earned on first unit = Rs. $$(130x - 100x) = 30x$$

Now, loss incurred is one-third of the profit

=> Loss incurred on second unit = Rs. $$\frac{30x}{3} = 10x$$

=> S.P. of second unit = Rs. $$(100x - 10x) = 90x$$

Thus, total S.P. of both units = $$130x + 90x = 220x$$

$$\therefore$$ Overall profit % = $$\frac{220x - 200x}{200x} \times 100$$

= $$\frac{20}{2} = 10 \%$$