Question

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

Answer 1

Let two consecutive natural numbers = x, x + 1

$\therefore$ One-fourth of the smaller = $\frac{x}{4}$

One-fifth of the greater = $\frac{x+1}{5}$

According to the statement :

$\frac{x}{4}=\frac{x+1}{5}+1\Rightarrow \frac{x}{4}-\frac{x+1}{5}=1\Rightarrow \frac{5x-4(x+1)}{20}=1\Rightarrow \frac{5x-4x-4}{20}=1\Rightarrow \frac{x-4}{20}=1\Rightarrow x-4=20\text{(Cross-multiplying)}\Rightarrow x=20+4\Rightarrow x=24\therefore x+1=24+1=25\therefore \text{Two consecutive numbers are 24 and 25}$