Working 12 hours per day, Raj can complete a work in 12 days. How many hours per day should he work so as to finish the same work in 9 days?

16 hours

The formula for work is $\frac{M \times H \times D}{Work}$ = Constant

M = no. of men, H = hourse worked per day, D = no. of days

Thus, for the same man doing the same job,

Hours x Days = constant

Then, to complete the work in 9 days,

12 x 12 = Hours x 9

Hours = 16