Given:

Total time by pipe A, B, and C together filled the tank = 10 hrs

A is thrice as fast as B

B is twice as fast as C

Concept used:

Time = 1/Efficiency

Calculation:

The efficiency of A = 3 × Efficiency of B

(Efficiency of A)/(Efficiency of B) = 3/1      ----(1)

The efficiency of B = 2 × Efficiency of C

(Efficiency of B)/(Efficiency of C) = 2/1      ----(2)

Combining Eqn. (1) and (2)

Efficiency ratio of A, B, and C = 6 ∶ 2 ∶ 1

Time ratio of A, b, and C = 1/6 ∶ 1/2 ∶ 1

⇒ Time ratio of A, b, and C = 1 ∶ 3 ∶ 6

Let the time taken by A, B, and C to fill the tank alone is x hrs, 3x hrs, and 6x hrs.

The volume of the tank filled in 1-hrs by A = 1/x

The volume of the tank filled in 1-hrs by B = 1/3x

The volume of the tank filled in 1-hrs by C = 1/6x

The volume of the tank filled by A, B, and C together in 1-hrs = 1-hrs volume by A + 1-hrs volume by B + 1-hrs volume by C

⇒ 1/10 = 1/x + 1/3x + 1/6x

⇒ 1/10 = (6 + 2 + 1)/6x

⇒ 1/10 = 9/6x

⇒ 6x = 90

⇒ x = 15 hrs

Total time by pipe B alone to fill the tank = 3x

⇒ Total time by pipe B alone to fill the tank = 3 × 15

⇒ Total time by pipe B alone to fill the tank = 45 hrs.

∴ The total time by pipe B alone to fill the tank is 45 hrs.