Two pipes A and B can fill a tank in 16 hrs and 12 hrs respectively. The capacity of the tank is 240 liters. Both the pipes are opened simultaneously and closed after 2 hrs. How much more water need to fill the tank?

Options

A. A) 70 lit
B. B) 170 lit
C. C) 90 lit
D. D) 190 lit

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the rate of filling for each pipe.
- **Pipe A** can fill the tank in 16 hours. Therefore, the rate of Pipe A is:
\[ \text{Rate of A} = \frac{240 \text{ liters}}{16 \text{ hours}} = 15 \text{ liters per hour} \]

- **Pipe B** can fill the tank in 12 hours. Therefore, the rate of Pipe B is:
\[ \text{Rate of B} = \frac{240 \text{ liters}}{12 \text{ hours}} = 20 \text{ liters per hour} \]

### Step 2: Calculate the combined rate of both pipes.
- When both pipes A and B are opened simultaneously, their combined rate is:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = 15 \text{ liters/hour} + 20 \text{ liters/hour} = 35 \text{ liters/hour} \]

### Step 3: Calculate the total amount of water filled in 2 hours.
- If both pipes are open for 2 hours, the total amount of water filled is:
\[ \text{Water filled in 2 hours} = \text{Combined Rate} \times 2 \text{ hours} = 35 \text{ liters/hour} \times 2 \text{ hours} = 70 \text{ liters} \]

### Step 4: Calculate the remaining water needed to fill the tank.
- The total capacity of the tank is 240 liters. After 2 hours, the amount of water filled is 70 liters. Therefore, the remaining water needed is:
\[ \text{Remaining Water} = \text{Total Capacity} - \text{Water Filled} = 240 \text{ liters} - 70 \text{ liters} = 170 \text{ liters} \]

### Final Answer:
The amount of water needed to fill the tank is **170 liters**.

---