6 men and 4 boys can finish a work in 20 days, and the same is finished in 24 days by 4 men and 6 boys. In how many days can 2 boys and 1 man finish the work?

Correct option is C

Given:

6 men and 4 boys can finish a work in 20 days.

4 men and 6 boys can finish same work in 24 days

Formula Used:

Work done = Number of workers $$\times$$​ Efficiency of each worker$$\times$$​ Time

Solution:

Let the efficiency of a man and a boy be M and B respectively.

According to the question,

​$$(6\times M + 4 \times B) \times 20 = (4 \times M + 6 \times B ) \times 24$$​​

​$$3M =8B$$​​

Total work is:

​$$= (6\times \frac{8B}{3} + 4 \times B) \times 20$$​​

​$$= 20B \times 20$$ 

​$$= 400B$$​​

2 boys and 1 men will complete the work in:

​$$2B + 1M = 2B + \frac{8B}{3} = \frac{14B}{3}$$ 

Time taken by 2 boys and 1 men will be =$$\frac{400B}{\frac{14B}{3}} = 85.71days$$