Pipe A can fill a tank of capacity 350 litres in `3(1/2)` minutes. Pipe B can fill a tank of capacity 780litres in `8(2/3)`minutes. How long (in min)will it take to fill a tank of capacity 1615 litres, if both pipes are opened together?

Options

A. 9
B. `7(1/2)`
C. `8(1/2)`
D. 8

Answer

To solve the problem step by step, we will first determine the efficiencies of both pipes A and B, and then calculate how long it will take to fill a tank of 1615 liters when both pipes are opened together.

### Step 1: Determine the efficiency of Pipe A
- Pipe A can fill a tank of 350 liters in 3.5 minutes.
- Efficiency of Pipe A = Work done / Time taken
- Efficiency of Pipe A = 350 liters / 3.5 minutes
- To simplify:
\[ \text{Efficiency of A} = \frac{350}{3.5} = \frac{3500}{35} = 100 \text{ liters per minute} \]

### Step 2: Determine the efficiency of Pipe B
- Pipe B can fill a tank of 780 liters in 8 and \( \frac{2}{3} \) minutes.
- Convert \( 8 \frac{2}{3} \) minutes into an improper fraction:
\[ 8 \frac{2}{3} = \frac{26}{3} \text{ minutes} \]
- Efficiency of Pipe B = Work done / Time taken
- Efficiency of Pipe B = 780 liters / \( \frac{26}{3} \) minutes
- To simplify:
\[ \text{Efficiency of B} = 780 \times \frac{3}{26} = \frac{2340}{26} = 90 \text{ liters per minute} \]

### Step 3: Calculate the combined efficiency of both pipes
- Combined efficiency = Efficiency of A + Efficiency of B
- Combined efficiency = 100 liters/minute + 90 liters/minute = 190 liters/minute

### Step 4: Calculate the time taken to fill the tank of 1615 liters
- Time taken = Work done / Combined efficiency
- Time taken = 1615 liters / 190 liters/minute
- To simplify:
\[ \text{Time taken} = \frac{1615}{190} = 8.5 \text{ minutes} \]

### Final Answer
Thus, it will take **8.5 minutes** to fill a tank of capacity 1615 liters if both pipes are opened together.

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