A and B can do a job in 12 days. B and C can do the job in 16 days. After A has worked for 5 days and B has worked for 7 days, C can finish the rest in 13 days. In how many days can C do the work alone?
Answer:
1/A + 1/B = 1/12 --------------(1)
1/B + 1/C = 1/16 --------------(2)
5/A + 7/B + 13/C =1 -----------(3)
Add (1) x 5 + (2) x 2, we get
5/A + 5/B + 2/B + 2/C = 5/12 + 2/16
or, 5/A + 7/B + 2/C = 26/48
or, 5/A + 7/B = 26/48 - 2/C ---------(4)
Substitute (4) in ((3)
26/48 -2/C + 13/C = 1
or, 11/C = 1-26/48 = 22/48
or, C = 48 x 11/22 = 24 days
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Answer:
1/A + 1/B = 1/12 --------------(1)
1/B + 1/C = 1/16 --------------(2)
5/A + 7/B + 13/C =1 -----------(3)
Add (1) x 5 + (2) x 2, we get
5/A + 5/B + 2/B + 2/C = 5/12 + 2/16
or, 5/A + 7/B + 2/C = 26/48
or, 5/A + 7/B = 26/48 - 2/C ---------(4)
Substitute (4) in ((3)
26/48 -2/C + 13/C = 1
or, 11/C = 1-26/48 = 22/48
or, C = 48 x 11/22 = 24 days
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