Joey completed the school project in 15 days. How many days will Tim take to complete the same work if he is 25% more efficient than Joey?

The correct answer is 12 days.

Step 1: Understand the given information

Let the total work to be completed be represented as 1 unit.

Joey completes the entire project in 15 days.

Therefore, Joey's work rate per day is:

$\text{Joey's daily work}=\frac{1}{15}$

Step 2: Calculate Tim's efficiency and daily work rate

Tim is 25% more efficient than Joey. This means Tim's work rate per day is 125% (or 1 + 0.25 = 1.25) of Joey's daily work rate.

$\text{Tim's daily work}=\frac{1}{15}\times \left(1+\frac{25}{100}\right)$

$\text{Tim's daily work}=\frac{1}{15}\times \frac{125}{100}$

Simplifying $\frac{125}{100}$ gives $\frac{5}{4}$:

$\text{Tim's daily work}=\frac{1}{15}\times \frac{5}{4}=\frac{1}{12}$

Step 3: Determine the total time taken by Tim

Since Tim completes $\frac{1}{12}$ of the work in 1 day, the total number of days required by Tim to complete the whole work is the reciprocal of his daily work rate:

$\text{Time taken by Tim}=\frac{1}{\left(\frac{1}{12}\right)}=12\text{days}$

Thus, Tim will take 12 days to complete the same work.