Question

Two consecutive natural numbers are such that two-fifths of the smaller is six less
than five-ninths of the larger.​

Answer 1

Answer:

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

⇒ (5x – 4 (x + 1))/20 = 1 ⇒ ((5x – 4x – 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