The ratio of the time taken by Worker A to Worker B to complete a specific project is 5 : 3. If Worker B can finish the entire project working alone in 15 hours, how long will it take for Worker A and Worker B to complete the project together?

The correct option is 9.375 hrs.

Step 1: Calculate the time taken by Worker A to complete the project alone.
We are given that the ratio of the time taken by Worker A to Worker B is 5 : 3, and Worker B can complete the project alone in 15 hours.
Let the time taken by Worker A be $T_A$ hours.
Setting up the proportion using the given ratio:

$\frac{T_A}{15}=\frac{5}{3}$

Solving for $T_A$:

$T_A=15\times \frac{5}{3}=25$ hours

So, Worker A takes 25 hours to complete the project alone.

Step 2: Determine the individual work rates of Worker A and Worker B.
The work rate per hour represents the fraction of the total project completed in one hour.
Worker A's rate per hour = $\frac{1}{25}$
Worker B's rate per hour = $\frac{1}{15}$

Step 3: Find the combined work rate when working together.
Add the work rates of Worker A and Worker B to find their joint progress in one hour:

$\text{Combined Rate}=\frac{1}{25}+\frac{1}{15}$

Find the least common multiple (LCM) of 25 and 15, which is 75:

$\text{Combined Rate}=\frac{3}{75}+\frac{5}{75}=\frac{8}{75}$

Together, Worker A and Worker B complete $\frac{8}{75}$ of the project per hour.

Step 4: Calculate the total time needed to finish the project together.
The time required to complete 1 whole project is the reciprocal of the combined work rate:

$\text{Total Time}=\frac{1}{8/75}=\frac{75}{8}$ hours

Converting the fraction into a decimal:

$\frac{75}{8}=9.375$ hours

Thus, it will take Worker A and Worker B 9.375 hrs to complete the project together.