Let the two parts be x and y.
Given:
x+y=141
According to the question:
8x:9y=5:6
So,
9y8x=65
8x×y9=65
8y9x=65
Cross multiply:
9x×6=5×8y
54x=40y
27x=20y
x=2720y
Substitute into (x + y = 141)
2720y+y=141
2720y+27y=141
2747y=141
47y=141×27
47y=3807
y=81
Now,
x=141−81=60
First part = 60