Answer:
C will take 96 days alone to do the work.
Explanation:
given,
A and B work for 12 days...................(1)
B and C work for 16 days...................(2)
C and A work for 24 days...................(3)
Adding equation (1) and (2)
[tex]A + 2 B + C = \dfrac{1}{12}+\dfrac{1}{16}\\2 B + \dfrac{1}{24}=\dfrac{1}{12}+\dfrac{1}{16}\\2B =\dfrac{1}{12}+\dfrac{1}{16}-\dfrac{1}{24}\\B=\dfrac{5}{96}[/tex]
from equation (2)
[tex]B+C = \dfrac{1}{16}\\\dfrac{5}{96}+C = \dfrac{1}{16}\\C=\dfrac{1}{16}-\dfrac{5}{96}\\C=\dfrac{1}{96}[/tex]
hence, C will take 96 days alone to do the work.
