**(a) 4 days**

(b) 5 days

(c) 6 days

(d) 7 days

Explanation:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

Then, 6x + 8y = 1/10 and 26x + 48y = 1/2.

Solving these two equations, we get : x = 1/100 and y = 1/200.

(15 men + 20 boy)’s 1 day’s work = (15/100 + 20/200) = 1/4.

15 men and 20 boys can do the work in 4 days.