EPS

100/96 is the bonus fraction.
Bonus fraction = cum rights price/ ex rights price
cum rights price is the pre-issue market price.

ex rights price is calculated as follows:
4 shares @ 100cents = 400 cents
1 share @ 80 cents = 80 cents
5 shares……………….480 cents
[one share for every four held ]

ex rights price = 480 cents/5 shares =96 cents

weighted average number of shares
(number of shares before rights issue is multiplied by the bonus fraction.)

120m shares * (9/12) * (100/96) =93.75m shares
150m shares * (3/12) = 37.5m shares
TOTAL 131.25m shares

how to get 150m shares
(120m/4)*1 =30m [Rights Issue]
120m shares before rights issue + 30m shares Rights Issue = 150m shares

Rights issues combine the characteristics of issues at full market price and bonus issues. The number of shares before the rights issue must be adjusted for the bonus element in the rights issue. For this, we multiply by the bonus fraction.

weighted average….the shares are weighted on a time basis, i.e., taking account of the date any new shares are issued during the year.
(i am sry…can’t explain more.)
here, we are calculating number of shares, not share price.

take a real life example,

person x bought
10 books @ 10
10 books @9 (on sales day)

avg cost of 20 books = (100+90)/20=95

but at price 9, how many books could have bought for 100,

10 books *10/9=11.111 books

then total cost of all these books,

11.111*9=99.99999==100
10*9=90
total cost =190
which is same as original cost.

in your example,120m *100/96, to get equivalent no. of shares at new price.
and also they consider time apportionment, so, it became,
120m*9/12*100/96.