ArithmeticIf A and B together can complete a work in 12 days, A and C together in 15 days and B and C together in 18 days, then how long they can do the complete work

If A and B together can complete a work in 12 days, A and C together in 15 days and B and C together in 18 days, then how long they can do the complete work

A
9.7 days
B
10.4 days
C
8.8 days
D
8.6 days

Solution:

A & B one day work = $\frac{1}{12}$

A & C one day work = $\frac{1}{15}$

B & C one day work = $\frac{1}{18}$

A, B & C's one day work = $\frac{1}{2} (\frac{1}{12} + \frac{1}{15} + \frac{1}{18})$

$= \frac{1}{2} (\frac{15 + 12 + 10}{180}) = \frac{37}{360}$

A, B & C can complete the work in $= \frac{360}{37} = 9.7 d a y s$