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

∴ One-fourth of the smaller = `"x"/4`

one-fifth of the greater = `("x" + 1)/5`

According to the statement:

 

`"x"/4 = ("x" + 1)/5 + 1 => "x"/4 - ("x" + 1)/5 = 1`

 

`=> (5"x" - 4("x" + 1))/20 = 1 => (5"x" - 4"x" - 4)/20 = 1`

 

`=> ("x" - 4)/20 = 1`

⇒ x - 4 = 20  ...(Cross multiplying)

⇒ x = 20 + 4 ⇒ x = 24

∴ x + 1 = 24 + 1 = 25

Two consecutive numbers are 24 and 25