Correct Answer - Option 2 : 45 hrs
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.
