Reinforcement needed

Let the total man-hours of the contract be $W$ , then, we have:

$\begin{aligned} \frac{4}{7}W & = 117 \times 33 \times 8 = 30888 \text{ man-hours} \\ \Rightarrow W & = \frac{30888 \times 7}{4} = 54054 \text{ man-hours} \end{aligned}$

• Remaining man-hours required $W_r = 54054-30888 = 23166 \text{ man-hours}$
• Number of 9-hour-man-days required $W_d = 23166 \div 9 = 2574 \text{ man-days}$
• Number of men required $M = 2574 \div (46-33) = 198 \text{ men}$
• Extra men required $M - 117 = 198 - 117 = \boxed{81} \text{ men}$