A number when increased by 23% becomes 861; find the number.

Let the number be $x$.

The number is increased by 23%.

∴ Amount by which the number is increased = 23% of $x$

= $\dfrac{23}{100} \times x$

= $\dfrac{23x}{100}$

Given, the increased number becomes 861,

$\therefore x + \dfrac{23x}{100} = 861 \\[1em] \Rightarrow \dfrac{100x + 23x}{100} = 861 \\[1em] \Rightarrow \dfrac{123x}{100} = 861 \\[1em] \Rightarrow x = \dfrac{861 \times 100}{123} \\[1em] \Rightarrow x = \dfrac{86,100}{123} \\[1em] \Rightarrow x = 700$

Hence, the number is 700.