Question: When a natural number is decreased by 20, the result is 96 times the reciprocal of the number. Find the number.

Solution:

Let x be the natural number. [ Natural number did always positive. ]

According to the question,

When a natural number is decreased by 20, the result is 96 times the reciprocal of the same number.

$or, x - 20 = 96 × \dfrac{1}{x}$

$or, x (x -20) = 96$

$or, x^2 -20x -96 = 0$

$or, x^2 - (24-4)x -96 = 0$

$or, x^2 -24x +4x -96 = 0$

$or, x(x -24) + 4(x -24) = 0$

$or, (x +4)(x -24) = 0$

Either,
$x +4 = 0$
$\therefore x = -4$

Or,

$x -24 = 0$
$\therefore x = 24.

Since, a natural number is always positive, the required nunber is 24.