Question

what number is that of which the third part exceeds the fifth part by 4

Answer 1

Let the number be x
Third part of it = $\frac{x}{3}$
Fifth part of it = $\frac{x}{5}$

Given that, the third part exceeds the fifth part by 4

$\frac{x}{3} - \frac{x}{5} = 4$

$\frac{5x-3x}{15} = 4$

2x = 60

x = 30

The number is 30

Verification:

Third part of 30 = 10
Fifth part of 30 = 6
The difference = 4

Answer 2

Answer :
    let the Number be x .
Therefore ,
   1/3x = 1/5x+4
x/3=x/5+4
or x/3=(x+4*5)/5
or x/3 = (x+20)/5
By Cross Multiplication , we get
or 5x = 3(x+20)
or 5x=3x+3*20
or 5x =3x+60
or 5x - 3x =60
or 2x = 60
or x=60/2
or x=30
hence the Number is 30 .

Hope This helps you!!
NOte :-
You can check your answer here 
   1/3*30 =10 
and 1/5*30 = 6 
therefore , 10  - 6 = 4