A contractor decided to complete a work in 80 days and employed 60 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed the additional men, how many extra days would he have needed to complete the work (round off to the nearest integer)?

20 days

Formula to be used here,

\( {M }_{1 } \) x \( {D }_{1 } \) = \( {M }_{2 } \) x \( {D}_{2 } \),

where, \( {M }_{1 } \) = Initial no. of men, \( {M }_{2 } \) = total men after employement after 20 days. 

\( {D }_{1 } \) = no. of days if extra men were not employed, \( {D }_{2 } \) = No. of days it took to complete the work with extra men.

⇒ 60 x \( {D }_{1 } \) = 80 x 60 

⇒ \( {D }_{1 } \) = 80 days. 

⇒ Extra days = 80 - 60 = 20 days