If 6 men and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do the same in 2 days, the time taken by 25 boys in doing the same type of work will be:

Given:

6 men and 8 boys can do a piece of work in 10 days.

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

Formula Used:

Work done (W) = Number of workers × Time

Calculation:

Let's assume 1 man's 1 day work = M and 1 boy's 1 day work = B.

We have two equations:

6M + 8B = W/10 ⇒ 60M + 80B = W ---- (1)

26M + 48B = W/2 ⇒ 52M + 96B = W ---- (2)

Equating both equations:

60M + 80B = 52M + 96B

⇒ 8M = 16B

⇒ M = 2B

Substituting M = 2B in equation (1):

60(2B) + 80B = W

⇒ 120B + 80B = W

⇒ 200B = W

Now, we need to find the time taken by 25 boys to complete the work:

Work done by 25 boys in 1 day = 25B

Total Work = 200B

Time taken by 25 boys = Total Work / Work done per day

⇒ Time = 200B / 25B

⇒ Time = 8 days

The correct answer is option 4.