3 men and 4 boys do a piece of work in 8 days, while 4 men and 4 boys finish it in 6 days. 2 men and 4 boys will finish it in:

Correct option is C

Given:
3 men and 4 boys do a piece of work in 8 days,
while 4 men and 4 boys finish it in 6 days.
Concept Used:
The rate of work of each person is the reciprocal of the time they take to complete the work. example,
A complete work in x day,
Rate of work in one day = $$\frac{1}{x}$$ day

Solution:
Let Man for M and Boys for B,​
​$$3M + 4B = \frac{1}{8}$$ .....(1)

​$$4M + 4B = \frac{1}{6}$$​.....(2)

Subtract the 1st equation from the 2nd:

3M + 4B - 4M - 4B =  $$\frac{1}{8} - \frac{1}{6}$$

​$$-M = \frac{3-4}{24}​​$$

​$$-M = \frac{-1}{24}​​$$

$$M = \frac{1}{24}$$

Substitute M = $$\frac{1}{24}$$  into 3M + 4B = $$\frac{1}{8}$$

$$3 \times \frac{1}{24} + 4B = \frac{1}{8}$$

$$\frac{1}{8} + 4B = \frac{1}{8}$$

4B = 0
B = 0
So,

$$2M + 4B = \left(2 \times \frac{1}{24} + 4 \times 0\right)​​​​​​$$

$$​2M + 4B = \frac{1}{12}$$

So, 2 men and 4 boys will finish the work in 12 days.
Thus, the correct answer is (c).​