A and B can do a piece of work in 15 days. B and C can do the same work in 10 days and A and C can do the same in 12 days. Time taken by A, B and C together to do the job is:

Let the total work = W

Number of days required for A and B to complete the work = 15 days

$$=$$>  Work done by A and B in 1 day = $$\frac{W}{15}$$

$$=$$>  A + B = $$\frac{W}{15}$$ ............................(1)

Number of days required for B and C to complete the work = 10 days

$$=$$> Work done by B and C in 1 day = $$\frac{W}{10}$$

$$=$$> B + C = $$\frac{W}{10}$$ .............................(2)

Number of days required for A and C to complete the work = 12 days

$$=$$> Work done by A and C in 1 day = $$\frac{W}{12}$$

$$=$$> A + C = $$\frac{W}{15}$$ .............................(3)

Adding equations (1), (2) and (3)

2A + 2B + 2C = $$\frac{W}{15}+\frac{W}{10}+\frac{W}{12}$$

$$=$$>  2(A + B +C) = $$\frac{4W+6W+5W}{60}$$

$$=$$>  2(A + B +C) = $$\frac{15W}{60}$$

$$=$$>  2(A + B +C) = $$\frac{W}{4}$$

$$=$$>  A + B + C = $$\frac{W}{8}$$

Work done by A, B and C in 1 day = $$\frac{W}{8}$$

$$\therefore\ $$Number of days required for A, B and C to complete the work = $$\frac{W}{\frac{W}{8}}=8$$ days

Hence, the correct answer is Option D