Akhil can complete a piece of work in 24 days. Shyam can complete the same piece of work in 12 days. If both of them work together, in how many days can they complete the same piece of work?

The correct answer is 8 days.

Step-by-Step Explanation:

Step 1: Determine the individual work done per day.
Let the total work to be completed be represented as 1 unit.

Akhil can complete the entire work in 24 days.
Therefore, Akhil's work rate per day = $\frac{1}{24}$

Shyam can complete the entire work in 12 days.
Therefore, Shyam's work rate per day = $\frac{1}{12}$

Step 2: Calculate their combined work rate per day.
When Akhil and Shyam work together, their combined work done in 1 day is the sum of their individual daily work rates:

$\text{Combined Work per Day}=\frac{1}{24}+\frac{1}{12}$

To add these fractions, find a common denominator, which is 24:

$\frac{1}{12}=\frac{2}{24}$

$\text{Combined Work per Day}=\frac{1}{24}+\frac{2}{24}=\frac{3}{24}$

Simplifying $\frac{3}{24}$ gives:

$\text{Combined Work per Day}=\frac{1}{8}$

Step 3: Calculate the total time required to complete the work together.
The number of days required to complete the total work working together is the reciprocal of their combined daily work rate:

$\text{Total Days}=\frac{1}{1/8}=8\text{days}$

Thus, working together, Akhil and Shyam can complete the work in 8 days.