12 men can do a piece of work in 15 days and 20 women can do the same work in 12 days. In how many days can 5 men and 5 women complete the same work ?

Solution(By Examveda Team)

12 man × 15 = 20 women × 12 = Total work
3 man = 4 women
$$\eqalign{ & \frac{{{\text{Men}}}}{{{\text{Women}}}} = \frac{4}{3} \to {\text{Efficiency}} \cr & {\text{Total work}} = 12 \times 4 \times 15 = 720 \cr & \left( {5{\text{ man}} + 5{\text{ women}}} \right) \times {\text{D}} = 720 \cr & {\text{D}}\left( {5 \times 4 + 5 \times 3} \right) = 720 \cr & {\text{D}} = \frac{{720}}{{35}} = 20\frac{4}{7}{\text{ days}} \cr} $$

---

Alternate:
According to the question,
12 men can do the 1 day work in $$\frac{1}{{15}}$$ days
So, 1 men can do the 1 day work in $$\frac{1}{{15 \times 12}}$$  = $$\frac{1}{{180}}$$ days
5 men can do the 1 day work in $$\frac{1}{{180}} \times 5$$   = $$\frac{5}{{180}}$$ days
Similarly 5 women do the 1 dys work $$\frac{5}{{240}}$$ days
∴ 5 men & 5 women together work in 1 day
$$\eqalign{ & = \frac{5}{{180}} + \frac{5}{{240}} \cr & = \frac{{20 + 15}}{{720}} \cr & = \frac{{35}}{{720}} \cr} $$
Hence, they complete the work $$\frac{{720}}{{35}}$$ = $$20\frac{4}{{35}}$$ days