Question

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

Answer 1

let x be smaller
and x + 1 be bigger ,



1/4 of x = 1 + 1/5 of (x + 1)

x/4 = 1 + (x+1)/5..............(1)

x = 4[ 1 + (x+1)/5]
    = 4 + (4x + 4)/5
    = (20 + 4x + 4)/5
x =(24 +4x)/5
  from (1)

(24 +4x)/5 = 1  + (x + 1)/5 
(24 + 4x) /5= (5 + x + 1)/5
24 + 4x = 6 + x
18 + 3x =0
3x = -18 
x = -6