8 men and 4 women together can complete a piece of work in 6 days. The work done by a man in one day is twice the work done by a woman in one day. Initially, 8 men and 4 women start working. After 2 days, 4 men leave and 4 new women join the work.

Compare the following quantities:

Quantity I: Additional days required to complete the work after the change
Quantity II: 5 days

Question

8 men and 4 women together can complete a piece of work in 6 days. The work done by a man in one day is twice the work done by a woman in one day. Initially, 8 men and 4 women start working. After 2 days, 4 men leave and 4 new women join the work.

Compare the following quantities:

Quantity I: Additional days required to complete the work after the change
Quantity II: 5 days

Accepted Answer

**Solution:**

1. Let the work done by one woman in one day be *w* units. Then, work done by one man in one day is *2w* units.

2. Total work done by 8 men and 4 women in one day:
   - Work by 8 men = $8 	imes 2w = 16w$
   - Work by 4 women = $4 	imes w = 4w$
   - Total daily work = $16w + 4w = 20w$

3. Since 8 men and 4 women complete the work in 6 days, total work = $20w 	imes 6 = 120w$

4. Work done in first 2 days by 8 men and 4 women:
   - $20w 	imes 2 = 40w$

5. Remaining work after 2 days:
   - $120w - 40w = 80w$

6. After 2 days, 4 men leave and 4 women join, so now:
   - Men = 4 men, work per day = $4 	imes 2w = 8w$
   - Women = 8 women, work per day = $8 	imes w = 8w$
   - Total daily work now = $8w + 8w = 16w$

7. Days required to finish remaining work:
   - $\frac{80w}{16w} = 5$ days

8. Quantity I (additional days needed) = 5 days
   Quantity II = 5 days

**Answer:** Quantity I = Quantity II (Option a)

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