A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?

Correct option is C

Given:
A + B can complete the work in 20 days → A + B = 1/20 work/day
B + C can complete the work in 30 days → B + C = 1/30 work/day
A + C can complete the work in 24 days → A + C = 1/24 work/day

Formula/Concept:
To find A alone's work/day:
A = (A + B + C) − (B + C)
We first calculate A + B + C by adding the three equations:
(A + B) + (B + C) + (A + C) = 2A + 2B + 2C = sum
Then divide by 2 to get A + B + C
Solution:

$$\textbf{} \\\text{(A + B)'s 1 day work} = \frac{1}{20} \\\ \\\text{(B + C)'s 1 day work} = \frac{1}{30} \\\ \\\text{(A + C)'s 1 day work} = \frac{1}{24} \\[10pt]\text{Now, add (A + B) and (B + C):} \\\ \\\frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12} \\[10pt]\text{(A + B + B + C) - (A + C) = 2B} \\\ \\\Rightarrow \frac{1}{12} - \frac{1}{24} = \frac{2 - 1}{24} = \frac{1}{24} \\\ \\\Rightarrow 2B = \frac{1}{24} \Rightarrow B = \frac{1}{48} \\[10pt]\text{Now substitute B into (A + B) = } \frac{1}{20} \\\ \\A + \frac{1}{48} = \frac{1}{20} \\\ \\A = \frac{1}{20} - \frac{1}{48} \\\ \\= \frac{12 - 5}{240} = \frac{7}{240} \\[10pt]\text{So, A alone can do the work in } \frac{240}{7} = 34\frac{2}{7} \text{ days}$$​​