Let x additional men employed.
117 men were supposed to finish the whole work in 46 × 8 = 368 hours.
But 117 men completed
of the work in 33 × 8 = 264 hours
∴ 117 men could complete the work in 462 hours.
Now (117 + x) men are supposed to do
of the work, working 9 hours a day, in 13 × 9 = 117 hours, so as to finish the work in time.
i.e. (117 + x) men are supposed to complete the whole work in 117 ×
= 273 hours.
∴ (117 + x) × 273 = 117 × 462
⇒ (117 + x) × 7 = 3 × 462
⇒ x + 117 = 3 × 66 = 198 ⇒ x = 81
∴ Required number of additional men to finish the work in time = 81.