8 men and 3 boys together can complete a piece of work in 5 days. If 5 boys can complete the same piece of work in 15 days, in how many days do 5 men complete the same piece of work?

The work involves 3 pieces of information:

• 8 men + 3 boys together finish work in 5 days
• 5 boys alone finish the same work in 15 days
• Need to find: 5 men alone will take how many days

---

5 boys finish the work in 15 days.

Total work $= 5 \times 15 = 75$ boy-days

One boy's one day work $= \dfrac{1}{75}$ of total work

---

8 men + 3 boys finish work in 5 days.

Work by 8 men in 5 days $= 8 \times 5 = 40$ man-days

Work by 3 boys in 5 days $= 3 \times 5 = 15$ boy-days

Total work $= 40$ man-days $+ 15$ boy-days

Since total work $= 75$ boy-days:

$40$ man-days $+ 15$ boy-days $= 75$ boy-days

$40$ man-days $= 60$ boy-days

$1$ man-day $= 1.5$ boy-days

---

Total work $= 75$ boy-days

Converting to man-days:

Total work $= \dfrac{75}{1.5} = 50$ man-days

For 5 men:

Days needed $= \dfrac{50}{5} = 10$ days

---

Therefore, 5 men complete the same piece of work in 10 days.