Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.

Let the consecutive natural numbers be x and (x + 1).

So,

$\dfrac{1}{4} \times x - \dfrac{1}{5} \times (x + 1) = 1 \\[1em] ⇒ \dfrac{x}{4} - \dfrac{x + 1}{5} = 1 \\[1em]$

Since L.C.M. of denominators 5 and 4 = 20, multiply each term with 20 to get:

$⇒ \dfrac{x \times 20}{4} - \dfrac{(x + 1) \times 20}{5} = 1\times 20$

⇒ x $\times$ 5 - (x + 1) $\times$ 4 = 20

⇒ 5x - (4x + 4) = 20

⇒ 5x - 4x - 4 = 20

⇒ x - 4 = 20

⇒ x = 20 + 4

⇒ x = 24

Other number = (x + 1)

= 24 + 1

= 25

Hence, the numbers are 24 and 25.