Question

one fifth of a number increased by 5 is equal to 4 less than one fourth of that number find the number

Answer 1

let the number be x
1/5x +5=1/4x-4
x/5-x/4=-9
4x-5x/20= -9[ since lcm of 5 and 4=20]
-x=-9x20
x=180

Answer 2

let the number be x

one fifth of the number is increased by 5
$\frac{1}{5} x + 5$

one forth of the number decreased by 4

$\frac{1}{4} x - 4$

therefore,

$\frac{1}{5} x + 5 = \frac{1}{4}x - 4$

$\frac{x}{5} + 5 = \frac{x}{4} - 4$

$\frac{x + 25}{5} = \frac{x - 16}{4}$

$=4(x + 25) = 5( x - 16)$

$4x + 100 = 5x - 80$

$100 + 80 = 5x - 4x$
x = 180

the number is 180.