A number increased by 15% becomes 391. Find the number.

Let the number be $x$.

The number increased by 15%.

Hence,

⇒ $x + 15$% of $x = 391$

⇒ $x + \dfrac{15}{100} \times x = 391$

⇒ $x + \dfrac{3}{20} \times x = 391$

⇒ $\dfrac{20}{20} \times x + \dfrac{3}{20} \times x = 391$

⇒ $\dfrac{(20 + 3)}{20} \times x = 391$

⇒ $\dfrac{23}{20} \times x = 391$

⇒ $x = \dfrac{391 \times 20}{23}$

⇒ $x = \dfrac{7,820}{23}$

⇒ $x = 340$

Hence, the number is 340.