Hi, 

8 boys and 12 girls can finish the work in 10 days, while 6 boys and 8 girls can finish it in 14 days

Note: work PER Day KEY

Let x and y represent work done per day by boy and girl respectively:

 8x + 12y = 1/10     

 6x  + 8y = 1/14    |multiplying thru by -3/2 to  eliminate the y variable



 8x + 12y = 1/10     

-9x  -12y = -3/28    |result of multiplying thru by -3/2 to  eliminate the y variable

     x = 1/140  and y = 1/280, work PER Day by each

time taken by 1 boy alonedays and 1 girl alonedays to finish the work. 

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