Two software developers, Alice and Bob, can finish a coding project in 17 days, whereas Alice, Bob, and Charlie working together can finish the same project in 12 days. Given that Alice is 60% more efficient than Charlie, calculate the number of days Bob would take to finish the entire project alone.

The correct option is 51 days.

Step 1: Calculate Charlie's 1-day work rate

Let the total project work be equal to 1 unit.

The combined 1-day work rate of Alice and Bob working together is:

$\text{Work rate of (Alice + Bob)}=\frac{1}{17}$

The combined 1-day work rate of Alice, Bob, and Charlie working together is:

$\text{Work rate of (Alice + Bob + Charlie)}=\frac{1}{12}$

Subtracting the work rate of Alice and Bob from the combined work rate gives Charlie's 1-day work rate:

$\text{Charlie's work rate}=\frac{1}{12}-\frac{1}{17}=\frac{17-12}{204}=\frac{5}{204}$

Step 2: Calculate Alice's 1-day work rate

Given that Alice is 60% more efficient than Charlie, Alice's efficiency is 160% (or 1.6) of Charlie's efficiency:

$\text{Alice's work rate}=\frac{160}{100}\times \text{Charlie's work rate}$

$\text{Alice's work rate}=\frac{8}{5}\times \frac{5}{204}=\frac{8}{204}$

Step 3: Calculate Bob's 1-day work rate

We know the combined 1-day work rate of Alice and Bob is:

$\text{Alice's work rate}+\text{Bob's work rate}=\frac{1}{17}$

Substituting Alice's work rate into the equation:

$\frac{8}{204}+\text{Bob's work rate}=\frac{1}{17}$

Converting 1/17 to a fraction with a denominator of 204:

$\frac{1}{17}=\frac{12}{204}$

Solving for Bob's 1-day work rate:

$\text{Bob's work rate}=\frac{12}{204}-\frac{8}{204}=\frac{4}{204}=\frac{1}{51}$

Step 4: Determine the time Bob takes to finish the project alone

The total number of days taken by Bob alone is the reciprocal of his 1-day work rate:

$\text{Time taken by Bob}=\frac{1}{1/51}=51\text{days}$

Therefore, Bob will take 51 days to finish the entire project alone.