A and B together can do a peace of work in 12 days, which B and C toge

Hi,

I am not clear how to solve. can i get a better solution please ?

K

A and B together can do a peace of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days. In how many days C alone will do the work?

A. 13
B. 17
C. 19
D. 21
E. 24

A and B together can do a piece of work in 12 days => A+B =1/12 (1)
B and C together can do in 16 days => B+C=1/16 (2)
After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days => 5A+7B+13C = 1 (3)
In how many days C alone will do the work? => C=?

3 variables & 3 equations so solve C using the equations:
A+B =1/12 (1) => A=1/12 - B (4)
B+C=1/16 (2) => C=1/16-B (5)

Sub (4) & (5) into (3):
5(1/12 - B) +7B + 13(1/16-B) =1
B=1/48

Sub B=1/48 into (5):
C=1/16 - 1/48
C=1/24

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