A can complete a piece of work in 4 hours and B can complete it in 6 hours. In how much time (in hours) will they together complete the work?

The correct option is 2 hours 24 minutes.

Here is the step-by-step explanation to solve the problem:

Step 1: Determine the work done by A and B individually in 1 hour.
Let the total work to be completed be represented as 1 unit.
Since A can complete the entire work in 4 hours, the rate of work of A (work done by A in 1 hour) is:
$\text{Rate of A}=\frac{1}{4}$
Similarly, since B can complete the entire work in 6 hours, the rate of work of B (work done by B in 1 hour) is:
$\text{Rate of B}=\frac{1}{6}$

Step 2: Find their combined rate of work when working together.
When they work together, their combined rate per hour is the sum of their individual rates:
$\text{Combined Rate}=\frac{1}{4}+\frac{1}{6}$
To add these fractions, find the least common multiple (LCM) of 4 and 6, which is 12:
$\text{Combined Rate}=\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$
So, together they can complete $\frac{5}{12}$ of the work in 1 hour.

Step 3: Calculate the total time taken to complete the work together.
The time taken to complete the work is the reciprocal of their combined work rate:
$\text{Total Time}=\frac{1}{5/12}=\frac{12}{5}\text{hours}$

Step 4: Convert the total time from hours into hours and minutes.
Let's express the fraction as a mixed number:
$\frac{12}{5}=2\frac{2}{5}\text{hours}$
This represents 2 full hours and a fraction of $\frac{2}{5}$ of an hour.
To convert $\frac{2}{5}$ of an hour into minutes, multiply it by 60 (since 1 hour = 60 minutes):
$\frac{2}{5}\times 60=2\times 12=24\text{minutes}$
Therefore, A and B working together will complete the work in 2 hours 24 minutes.