If 6 men and 8 boys can complete a work in 10 days and 26 men and 48 boys can do it in 2 days, then find the ratio of capacity of a man to that of a boy.

6 men and 8 boys can complete the work in 10 days.

26 men and 48 boys can complete the work in 2 days.

Total work = (Number of men × Capacity of a man) + (Number of boys × Capacity of a boy)

Let the work done by 1 man in 1 day be m units and the work done by 1 boy in 1 day be b units.

From the first condition (6 men and 8 boys complete the work in 10 days):

​$$\text{Total Work} = 10 \times (6m + 8b) = 60m + 80b ...... \tag{1}$$​​

From the second condition (26 men and 48 boys complete the work in 2 days):

​$$\text{Total Work} = 2 \times (26m + 48b) = 52m + 96b...... \tag{2}$$​​

Equating both total works from equations (1) and (2) and simplifying:

60m + 80b = 52m + 96b

60m - 52m = 96b - 80b

8m = 16b

m=2b

​$$\frac{m}{b} = \frac{2}{1}$$​​

Therefore, the ratio of the capacity of a man to that of a boy is 2:1.