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.