Let the number be 'x'. x = ?

We have

(3/4) * x = 60 + (1/3)*x

If we multiply both sides of the equation by 12 we get

(3*12/4) * x = 60 * 12 + (12/3)*x

9x = 720 + 4x

9x - 4x = 720

5x = 720

x = 144

Indeed for x = 144 we have

3/4 of 144 is 108

1/3 of 144 is 48

And the difference between them is 108 - 48 = 60 as required.

The number is 144.