The cost price of an article is 30 percent less than its selling price. Find the profit or the loss as percent.

Given:

The C.P. of an article = $30\%$ less than its S.P.

Let the S.P. be ₹ $100$.

$\text{C.P.} = \text{S.P.} - \dfrac{30}{100} \times \text{S.P.}\\[1em] \text{C.P.} = ₹100 - \dfrac{30}{100} \times 100\\[1em] = ₹ 100 - \dfrac{30}{\cancel{100}}\times\cancel{100}\\[1em] = ₹ 100 - 30\\[1em] = ₹ 70$

(∵ S.P. is greater than C.P., means article is sold at profit.)

Profit = S.P. - C.P.

= ₹ 100 - ₹ 70

= ₹ 30

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\%\\[1em] = \dfrac{30}{70} \times 100\%\\[1em] = \dfrac{3,000}{70}\%\\[1em] = \dfrac{300}{7}\%\\[1em] = 42\dfrac{6}{7}\%$

Hence, Profit% = $42\dfrac{6}{7}\%$