Let's assume following variables/values

◉ Rate of A = A
◉ Rate of B = B
◉ Rate of C = C
◉ Work Done = 1 (As Work done by everyone is same)

Formula to be used Rate * Time = Work

A and B can complete a work in 10 days

=> Combined rate of A and B = A + B
=> Rate * Time = Work
=> (A + B) * 10 = 1
=> A + B = 1/10 ...(1)

B and C can complete the same work in 12 days

=> Combined rate of B and C = B + C
=> Rate * Time = Work
=> (B + C) * 12 = 1
=> B + C = 1/12 ...(2)

A and C can complete that work in 15 days

=> Combined rate of A and C = A + C
=> Rate * Time = Work
=> (A + C) * 15 = 1
=> A + C = 1/15 ...(3)

If A, B and C are working together, how many days does it take to complete the work?

=> Combined rate of A, B and C = A + B + C
=> Rate * Time = Work
=> (A + B + C) * Time = 1
=> Time = 1 / (A + B + C)

(1) + (2) + (3)
=> A + B + B + C + A + C = 1/10 + 1/12 + 1/15
=> 2 * (A + B + C) = 6/60 + 5/60 + 4/60 = 15/60 = 1/4
=> A + B + C = 1/(2*4) = 1/8

=> Time = 1/(A + B + C) = 1 / (1/8) = 8

So, Answer will be D
Hope it helps!

Watch following video to MASTER Work Rate Problems

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