Given:
A contractor employed 60 men to do a certain work in 50 days.
After 20 days, 20 men left the work, so he employed 20 women at that time.
Each woman works at 53 of the rate of each man,
Formula used:
Total units of work = M × D × E
Where,
M = number of manpower
D = number of days
E = Efficiency of each manpower
Calculation:
Let M and W are the efficiency of each man and each woman respectively.
Let the efficiency of each man = M = 5 units a day
According to the question,
Efficiency of each woman = W = 3/5 of M = 3 units a day
Scenario 1: A contractor employed 60 men to do a certain work in 50 days.
Total amount of work = 60 × 5 × 50 = 15000 units
Scenario 2: After 20 days, 20 men left the work.
Amount of work done in 20 days by 60 mens = 60 × 5 × 20 = 6000 units
Remaining work = 15000 - 6000 = 9000 units
Remaining days = 50 - 20 = 30 days
Scenario 3: After 20 days, 20 men left the work, so he employed 20 women at that time with 3/5 of the efficiency of each men.
Combined efficiency of 40 men and 20 women = C = 40M + 20W
⇒ C = (40 × 5) + (20 × 3) = 260 units a day
Remaining work = 9000 units
Days required to complete the work by 40 men and 20 women = 9000/260 = 34138 days
Extra days required = 34138 - 30 = 4138 days
Therefore, '4138 days' is the required answer.