Mitu can do a piece of work in 12 hours, Titu and Situ together in 2 hours, and Mitu and Situ together in 3 hours. How long will Titu alone take to do it?

The correct option is 4 hours.

Let's solve the problem step-by-step by defining the rate of work for each person in terms of the fraction of the total work they can complete in 1 hour.

Let the total work be represented as 1 unit.

Mitu can complete the work in 12 hours.
Therefore, Mitu's work rate ($R_M$) is:
$R_M=\frac{1}{12}$ of the work per hour.

Mitu and Situ together can complete the work in 3 hours.
Therefore, their combined work rate ($R_M+R_S$) is:
$R_M+R_S=\frac{1}{3}$ of the work per hour.

We can find Situ's work rate ($R_S$) by substituting Mitu's rate into the combined rate:
$\frac{1}{12}+R_S=\frac{1}{3}$
$R_S=\frac{1}{3}-\frac{1}{12}$
To subtract these fractions, we find a common denominator, which is 12:
$R_S=\frac{4}{12}-\frac{1}{12}=\frac{3}{12}=\frac{1}{4}$ of the work per hour.

Titu and Situ together can complete the work in 2 hours.
Therefore, their combined work rate ($R_T+R_S$) is:
$R_T+R_S=\frac{1}{2}$ of the work per hour.

Now, we can find Titu's work rate ($R_T$) by substituting Situ's rate ($R_S=\frac{1}{4}$) into this equation:
$R_T+\frac{1}{4}=\frac{1}{2}$
$R_T=\frac{1}{2}-\frac{1}{4}$
$R_T=\frac{2}{4}-\frac{1}{4}=\frac{1}{4}$ of the work per hour.

Since Titu's work rate is $\frac{1}{4}$ of the work per hour, the time taken by Titu alone to complete the entire work is:
$\text{Time}=\frac{1}{R_T}=\frac{1}{1/4}=4\text{hours}$.