If the purchasing price of 12 items is equal to the selling price of 9 items, then find the profit percentage.

Given: If the purchasing price of 12 items is equal to the selling price of 9 items.

Let, the cost price (CP) of one item be x.
Let, the selling price (SP) of one item be y.

The purchasing price of 12 items = Selling price of 9 items

12x = 9y

​$$\frac {y}{x}$$ = $$\frac {12}{9}$$ = $$\frac {4}{3}$$

y = $$\frac {4}{3}$$x

Profit % = $$\bigg(\frac {SP - CP}{CP}\bigg)$$ $$\times$$ 100

= $$\bigg(\frac {\frac {4}{3}x - x}{x}\bigg) \times$$ 100

= $$\bigg(\frac {\frac {4x - 3x}{3}}{x}\bigg) \times$$ 100

= $$\bigg(\frac {x}{3x}\bigg) \times$$ 100

= $$\frac {100}{3}$$

= $$33\frac {1}{3}$$ %

Thus, correct option is (a).