Question

Three pipes A, B, and C can fill a tank in 6 hrs. After working at it together for 2 hrs, C is closed and A and B can fill the remaining part in 7 hrs. The total number of hours taken by C alone to fill the tank is

• A. 14
• B. 12
• C. 11
• D. 10
• E. 13

Hint:

Use the work-rate equation to solve time-based problems. Divide the problem into parts and solve for each.

Answer 1

The Correct Option is A

Let the rate at which A, B, and C fill the tank be \( A \), \( B \), and \( C \) respectively. We know that: \[ \text{Time taken by A and B together to fill the tank} = 7 \text{ hrs} \] Total work done is 1 tank, and the combined rate of A and B can be calculated from the work done in 7 hrs. After working together for 2 hrs, the fraction of the tank filled is: \[ \text{Fraction filled in 2 hrs} = 2(A + B + C) \] After closing C, the remaining part is filled by A and B alone in 7 hrs. Solving for C: \[ C = 14 \]