4/7 of work is completed .
Remaining work=1- 4/7
=3/7
Remaining period= 46-33
=13 days
Less work, less men(direct proportion)
less days, more men(Indirect proportion)
More hours/day, less men(Indirect proportion)

work 4/7:3/7
Days 13:33 :: 117:x
hrs/day 9:8

(4/7)*13*9*x=(3/7)*33*8*117
x=(3*33*8*117) / (4*13*9)
x=198 men
So, additional men to be employed=198 -117=81

hey i started this way: just want to know where i am making a mistake and how to proceed.

117 men take 46 days to complete the work in 8 hours.
so in 1 day 117 men will complete 1/46 of the work.
in 33 days -> 33/46 of the work is over
This equal the 4/7th of the work completed, where x= total work.

4x/7 = 33/46

so x= 33*7/4* 46

now 3/7th of the work is left pending. ie. 3/7 ( 33*7/4*46) => 99/4*46

Let y people be needed to worked for 9 hours for the rest 13 days (this y includes 117. so i will subtract 117 from y to get the answer)

99/4*46 = y* 9* 13

y= 99/4*46*9*13

now this will not even give an integer value. i know i am making a miss somewhr.

fibbonnaci wrote:hey i started this way: just want to know where i am making a mistake and how to proceed.

117 men take 46 days to complete the work in 8 hours.

This is not stated in question.question says 117 men need to complete a piece of work in 46 days and they started to work for 8 days and finish 4/7 of work in 33 days.
so 117 men finish 4/7 of work in 33 x 8 man hours
rest of the calculation will follow from here.