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A and B together can complete a work in 12 days. B and C together can complete the same work in 8 days and A and C together can complete it in 16 days. In total, how many days do A, B and C together take to complete the same work ?

Correct Answer: $${\text{7}}\frac{5}{{13}}$$
$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{12}} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{8} \cr & \left( {{\text{A}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{{16}} \cr} $$
Adding, we get 2(A + B + C)'s 1 day's work
$$\eqalign{ & = \left( {\frac{1}{{12}} + \frac{1}{8} + \frac{1}{{16}}} \right) \cr & = \frac{{13}}{{96}} \cr} $$
So, A, B and C together can complete the work in
$$\eqalign{ & = \frac{{96}}{{13}} \cr & = 7\frac{5}{{13}}{\text{days}} \cr} $$

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