Let the time taken by man be x daystime taken by boys be y dayswork done by 1 man in one day=1/xwork done by 1 boy in one day=1/y8/x+12/y = 1/10............eq 16/x+ 8/y = 1/14..........eq2Let u=1/x & v=1/y8u+ 12y=1/10.........eq36u+8v= 1/14...........eq4Multiplying eq3 by 2 & eq4 by 3 16u+ 24y=2/10.........eq518u+24v= 3/14.........eq6subtract eq 5 & 6-2u= -3/14+2/10-2u = (-3×10 +2×14)/140-2u=( -30+28)/140-2u=-2/140u=1/140put this value in eq 516u+ 24y=2/1016×1/140 +24y =1/54/35+24y= 1/524y= 1/5-4/3524y= (1×7 -4)/3524y = (7-4)/3524y= 3/35y= 3/35×24y= 1/280u=1/x1/140 = 1/xx=140v=1/y1/280 = 1/yy=280A man complete the work in 140 daysA boy can complete the work in 280 daysOoops!! it seems little bit long.......

Let the time taken by one man alone to finish the work be "m" and the time taken by one boy alone to finish the work be "b".

We can set up the following two equations based on the given information:

1. 8m + 12b = 1/10 (the work done by 8 men and 12 boys in 10 days)
2. 6m + 8b = 1/14 (the work done by 6 men and 8 boys in 14 days)


We can solve the above two equations simultaneously to find the values of "m" and "b".

Multiplying the first equation by 7 and the second equation by 5, we get:

1. 56m + 84b = 7/10
2. 30m + 40b = 1/14

Now, we can use any method to solve these two equations. Here, we will use the elimination method.

Multiplying the second equation by 21, we get:

3. 630m + 840b = 3/14

Subtracting equation 1 from equation 3, we get:

4. 574m + 756b = 1/35

Multiplying equation 2 by 3, we get:

5. 18m + 24b = 3/42

Subtracting equation 5 from equation 4, we get:

6. 556m + 732b = 1/35 - 3/42

Simplifying, we get:

6. 556m + 732b = 1/210

Multiplying equation 2 by 7, we get:

7. 42m + 56b = 1/2

Subtracting equation 7 from equation 1, we get:

8. 14m + 28b = 1/10 - 1/2

Simplifying, we get:

8. 14m + 28b = -2/5

Multiplying equation 8 by 3, we get:

9. 42m + 84b = -6/5

Adding equation 9 to equation 6, we get:

10. 598m + 816b = -1/210

Multiplying equation 2 by 5, we get:

11. 30m + 40b = 5/70

Subtracting equation 11 from equation 7, we get:

12. 12m + 16b = 1/2 - 5/70

Simplifying, we get:

12. 12m + 16b = 3/7

Multiplying equation 12 by 3, we get:

13. 36m + 48b = 9/7

Subtracting equation 13 from equation 10, we get:

14. 562m + 768b = -16/210

Simplifying, we get:

14. 281m + 384b = -8/105

Multiplying equation 12 by 14, we get:

15.