Explanation
Let's denote the weight of the man in the stationary lift as W and the weight in the accelerating lift as W'.
We know that W' / W = 2/3.
When the lift is accelerating downward with acceleration 'a', the apparent weight (W') is given by:
W' = W - ma
where m is the mass of the man.
Since W' / W = 2/3, we can write:
(W - ma) / W = 2/3
Substitute W = mg (where g is the acceleration due to gravity):
(mg - ma) / mg = 2/3
Simplify:
g - a = (2/3)g
a = g - (2/3)g
a = (1/3)g
a = g/3