16 men can complete a work in 12 days. 12 women can complete the same work in 32 days. 16 men and 16 women together worked for 4 days, after which the women dropped out and 16 more men joined. In how many days will the men be able to complete the remaining work?

16 men can complete the work in 12 days.

12 women can complete the same work in 32 days.

16 men and 16 women worked together for 4 days, after which only men continued, with 16 additional men joining (total 32 men). 

Formula Used: 

Total work = Efficiency $$\times$$ No. of person $$\times$$ number of days

Solution: 

Let Efficiency of Men be m and efficiency of women be w 

Now, 

​$$16 \times m \times 12 = 12 \times w \times 32 \\ \implies \frac{m}{w} = \frac{2}{1}$$ 

Total work = $$16 \times 2\times 12 = 384 \,unit$$ 

Work completed by men and women in 4 days.

​$$(16 \times 2 + 16 \times 1) \times 4 = 192$$ 

Remaining work = 384 - 192 = 192 

time taken to complete the remaining work by 32 men 

 $$=\frac{192}{32\times 2} \\ = 3 \, days$$ 

Thus, remaining work is complete in 3 days.