In class X of a school, the ratio of the number of boys to that of the girls is 4 : 3. If there were 20 more boys and 12 less girls, then the ratio would have been 2 : 1. How many students were there in the class?

Ratio of the number of boys to girls is 4 : 3, so let the number of boys be 4x and number of girls be 3x.

According to question,

4x + 20 : 3x - 12 = 2 : 1

$\Rightarrow \dfrac{4x + 20}{3x - 12} = \dfrac{2}{1} \\[0.5em] \Rightarrow 4x + 20 = 2(3x - 12) \\[0.5em] \Rightarrow 4x + 20 = 6x - 24 \\[0.5em] \Rightarrow 6x - 4x = 20 + 24 \\[0.5em] \Rightarrow 2x = 44 \\[0.5em] \Rightarrow x = 22.$

∴ Total number of students = 4x + 3x = 7x = $7 \times 22$ = 154.

Hence, the total number of students are 154.