25 men can complete a task in 16 days. Four days after they started working, 5 more men, with equal workmanship, joined them. How many days will be needed by all to complete the remaining task?

Let the total work = W

25 men can complete the task in 16 days

$$=$$>  Number of days required for 25 men to complete the work = 16 days

$$=$$>  Work done by 25 men in 1 day = $$\frac{W}{16}$$

$$=$$>  Work done by 25 men in 4 days =$$4\times\frac{W}{16}=\frac{W}{4}$$

$$\therefore\ $$Remaining work = $$W-\frac{W}{4}=\frac{3W}{4}\ $$

Let the number of days required for 30 men to complete remaining work = $$d_2$$ days

We know that $$\frac{M_1d_1}{W_1}=\frac{M_2d_2}{W_2}$$

$$=$$>  $$\frac{25\times16}{W}=\frac{30\times d_2}{\frac{3W}{4}}$$

$$=$$>  $$\frac{25\times16}{W}=\frac{30\times d_2\times4}{3W}$$

$$=$$>  $$d_2=10$$ days

$$\therefore\ $$The number of days required for 30 men to complete remaining work = 10 days

Hence, the correct answer is Option A