Question 1039208
This is the same as any work rates problem;  RT=W to relate rate, time, amount of work.


Your description uses different amounts of workers of different types, and each one worker has its own rate.


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Change from:
8men and 12boy can finish a piece of work in 5 day  while 6men and 8boy can finish it in 7 day. Find the time taken by 1men and 1 boy alone 


To this:
Eight men and 12 boys can finish a piece of work in 5 days,  while 6 men and 8 boys can finish it in 7 days. Find the time taken by 1 man and 1 boy alone. 
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The amount of work in those two parts is  1, of whatever unit is this work.
Let r be the work rate for one man and let B be the work rate for one boy.
Rate of workers acting together is the addition of all their individual rates.
This is the basic system of equations according to the description:{{{system((8r+12B)5=1,(6r+8B)7=1)}}}



Can you understand, and then do the rest  (arithmetic)?