Problem: A and B together can do a job in 2 days; B and C can do it in four days; and A and C in 252 days. The number of days required for A to do the job alone is:
Answer Choices:
A. 1
B. 3
C. 6
D. 12
E. 2.8
Solution:
Denote by a,b,c the respective number of days it would take A,B,C to complete the job if he were working alone; then 1/a,1/b,1/c denote the fractions of the job done by each in one day. Since it takes A and B together two days to do the whole job, they do half the job in one day, ie.,
a1+b1=21, and similarly, b1+c1=41,a1+c1=125.
∴a1−b1=61,a2=32,a=3