Pumps A, B and C operate at their respective constant rates. Pumps A and B, simultaneously, can fill a certain tank in 6/5 hours. Pump A and C, operating simultaneously, can fill the tank in 3/2 hours; abd pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?

(A) 1/3
(B) 1/2
(C) 2/3
(D) 5/6
(E) 1

Correct answer: (E)

I am unable to deduce the correct solution.

remember that rate = reciprocal of time taken to complete one job.
also, remember that rates are additive, so rate(pumps a AND b) = rate(pump a) + rate(pump b).
so:
rate(pumps a AND b) = 5/6
rate(pumps a AND c) = 2/3
rate(pumps b AND c) = 1/2

using the above fact about additive rates,
rate(pump a) + rate(pump b) = 5/6
rate(pump a) + rate(pump c) = 2/3
rate(pump b) + rate(pump c) = 1/2

you know you want the rate for all three pumps. from the symmetry of the above equations, it becomes apparent that we can find this by adding together all 3 equations:
2rate(pump a) + 2rate(pump b) + 2rate(pump c) = 5/6 + 2/3 + 1/2 = 2
rate(pump a) + rate(pump b) + rate(pump c) = 1
rate(pumps a AND b AND c) = 1 (because rates are additive)
time = reciprocal of 1 = 1

Thanks a lot! I kept doing a lot of calculations and got things wrong.

I assumed that let A, B, C complete the job (indivisually) in a, b, c hours.

Hence their respective rates would be: 1/a, 1/b, 1/c

Then,
1/a + 1/b = 5/6
1/a + 1/c = 2/3
1/b + 1/c = 1/2

Then I was solving the 3 equations to get values of a, b, c. That consumed a lot of time and I had to guess the answer.

We're glad it makes sense now.