When a positive number is decreased by 4, it is equal to 21 times the reciprocal of the number. Find the number.

The correct answer is 7.

Let us suppose the positive number is x.

According to the question,

1. When a positive number is decreased by 4, the number becomes= x-4

2. 21 multiplied by reciprocal of that number becomes $$\frac{21}{x}$$

By the problem,

x- 4 = $$\frac{21}{x}$$

$${x^2}$$ - 4x - 21 =0

$${x^2}$$ -7x +3x -21 = 0

$$\left(x-7\right)\left(x+3\right)$$ =0

therefore x= 7 or x = -3. Since x is a positive integer, therefore x is 7