Sol : In this kind of questions we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers.
Therefore, 6B+8G = 6 days
=> 6(6B+8G)= 1 day (inversely proportional)
=> 36B+48G =1 ( by unitary method)
Again 14B+10G = 4days
=> 56B+40G =1
so, here it is clear that either we employ 36B and 48G to finish the work in 1 day or 56B and 40G to finish the same job in 1 day. thus , we can say
=> 36B+48G = 56B+40G
=> G= 2.5B
Thus a Girl is 2.5 times as efficient as a boy.
Now, since 36B+48G = 1
=> 36B+48(2.5 B)=1
i.e., to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days
Now, since 156 boys can finish the job in 1 day
so 1 boy can finish the job in 156 days
Therefore, 3.5 boys can finish the job in days.