Question

Pipe-1 can fill a tank in 17.5 minutes. Pipe-2 can fill the tank in 20 minutes. Both pipes can fill at the rate of 6 liters/sec. What is the capacity of the tank?

• A. 3360
• B. 3570
• C. 3670
• D. 3450

Hint:

When solving rate problems involving filling or emptying, always convert all time units to the same system (like seconds) and then add the rates together.

Answer 1

The Correct Option is A

Step 1: Convert the times to seconds.
- Pipe-1 fills the tank in 17.5 minutes. To convert this to seconds: \[ \text{Time for Pipe-1} = 17.5 \times 60 = 1050 \, \text{seconds} \] - Pipe-2 fills the tank in 20 minutes. To convert this to seconds: \[ \text{Time for Pipe-2} = 20 \times 60 = 1200 \, \text{seconds} \] Step 2: Calculate the flow rate of each pipe.
- The flow rate of Pipe-1 (liters per second) is: \[ \text{Flow rate of Pipe-1} = \frac{\text{Capacity of tank}}{\text{Time for Pipe-1}} = \frac{C}{1050} \] - The flow rate of Pipe-2 (liters per second) is: \[ \text{Flow rate of Pipe-2} = \frac{\text{Capacity of tank}}{\text{Time for Pipe-2}} = \frac{C}{1200} \] Step 3: Add the flow rates of both pipes.
Both pipes together fill at the rate of 6 liters per second: \[ \frac{C}{1050} + \frac{C}{1200} = 6 \] Step 4: Solve for \(C\).
To solve for \(C\), first find the least common denominator (LCD) of 1050 and 1200. The LCD is 4200, so: \[ \frac{4C}{4200} + \frac{3.5C}{4200} = 6 \] \[ \frac{7.5C}{4200} = 6 \] Multiply both sides by 4200: \[ 7.5C = 25200 \] \[ C = \frac{25200}{7.5} = 3360 \] Step 5: Conclusion.
The capacity of the tank is 3360 liters, which corresponds to option (1).