A positive number, when decreased by 4, is equal to 21 times the reciprocal of the number. The number is:

Question: A positive number, when decreased by 4, is equal to 21 times the reciprocal of the number. The number is:

Solution:
Let the number be x

ATQ,
x - 4 = 21/x
⇒ x(x - 4) = 21
⇒ x² - 4x - 21 = 0
⇒ x² - 7x + 3x - 21 = 0
⇒ x(x - 7) + 3(x - 7) = 0
∴ (x - 7)(x + 3) = 0
Now,
x - 7 = 0
∴ x = 7
Or
x + 3 = 0
∴ x = - 3

So the number = 7