A man sold an article for ₹ 396 and gained 10% on it. Find the cost price of the article.

Given:

S.P. = ₹ 396

Profit = 10%

Let the C.P. of the article be ₹ x.

As we know,

Profit % = $\dfrac{Profit}{C.P.} \times 100$

⇒ 10 = $\dfrac{Profit}{x} \times 100$

⇒ Profit = $\dfrac{10 \times x}{100}$

⇒ Profit = $\dfrac{10x}{100}$

⇒ Profit = $\dfrac{x}{10}$

And,

Profit = S.P. - C.P.

⇒ $\dfrac{x}{10}$ = 396 - x

⇒ $\dfrac{x}{10} + \dfrac{x}{1}$ = 396

Since L.C.M. of 10 and 1 = 10, multiply each term with 10 to get:

⇒ $\dfrac{1x \times 10}{10} + \dfrac{x \times 10}{1}$ = 396 $\times$ 10

⇒ 1x + 10x = 3960

⇒ 11x = 3960

⇒ x = $\dfrac{3960}{11}$

⇒ x = 360

Hence, cost price of the article is ₹ 360.