Taps A,B and C are attached with a tank and velocity of water coming through them are 42L/h , 56L/h and 48L/h , respectively. A and B are inlets and C is outlet. If all the taps are opened simultaneously, tank is filled in 16 h. What is the capacity of the tank?

Options

A. 2346 L
B. 1600 L
C. 800 L
D. 960 L

Answer

To solve the problem, we need to determine the capacity of the tank based on the flow rates of the taps and the time taken to fill the tank. Here’s a step-by-step solution:

### Step 1: Identify the flow rates of the taps
- Tap A fills at a rate of **42 L/h**.
- Tap B fills at a rate of **56 L/h**.
- Tap C empties at a rate of **48 L/h**.

### Step 2: Calculate the net flow rate when all taps are opened
Since taps A and B are filling the tank and tap C is emptying it, we need to calculate the net flow rate:

\[ \text{Net flow rate} = (\text{Flow rate of A} + \text{Flow rate of B}) - \text{Flow rate of C} \]

Substituting the values:

\[ \text{Net flow rate} = (42 \, \text{L/h} + 56 \, \text{L/h}) - 48 \, \text{L/h} \]

\[ \text{Net flow rate} = 98 \, \text{L/h} - 48 \, \text{L/h} = 50 \, \text{L/h} \]

### Step 3: Calculate the total time taken to fill the tank
The problem states that the tank is filled in **16 hours**.

### Step 4: Calculate the capacity of the tank
Now, we can calculate the capacity of the tank using the net flow rate and the time taken to fill it:

\[ \text{Capacity of the tank} = \text{Net flow rate} \times \text{Time} \]

Substituting the values:

\[ \text{Capacity of the tank} = 50 \, \text{L/h} \times 16 \, \text{h} \]

\[ \text{Capacity of the tank} = 800 \, \text{L} \]

### Final Answer
The capacity of the tank is **800 liters**.

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