Three beakers have capacity of 250ml, 650ml and 3 ml. 682 ml of Juice is poured into them so that the same fraction of each is filled. The volume filled in the largest beaker will be

Options

A. 415 ml
B. 403 ml
C. 400 ml
D. 424 ml

Answer

To solve the problem step by step, we need to determine how much juice is poured into each beaker, ensuring that the same fraction of each beaker is filled.

### Step 1: Define the variables
Let:
- \( a \) = volume of juice in the first beaker (250 ml)
- \( b \) = volume of juice in the second beaker (650 ml)
- \( c \) = volume of juice in the third beaker (300 ml)

### Step 2: Set up the ratio
Since the same fraction of each beaker is filled, we can express this relationship as:
\[ \frac{a}{250} = \frac{b}{650} = \frac{c}{300} = k \]
where \( k \) is the common fraction.

### Step 3: Express volumes in terms of \( k \)
From the ratio, we can express \( a \), \( b \), and \( c \) in terms of \( k \):
\[ a = 250k \]
\[ b = 650k \]
\[ c = 300k \]

### Step 4: Write the total volume equation
The total volume of juice poured into the beakers is given as 682 ml. Therefore, we can write:
\[ a + b + c = 682 \]
Substituting the expressions for \( a \), \( b \), and \( c \):
\[ 250k + 650k + 300k = 682 \]

### Step 5: Combine like terms
Combine the terms on the left side:
\[ (250 + 650 + 300)k = 682 \]
\[ 1200k = 682 \]

### Step 6: Solve for \( k \)
Now, solve for \( k \):
\[ k = \frac{682}{1200} \]
\[ k = \frac{341}{600} \]

### Step 7: Calculate the volumes in each beaker
Now we can find the volume in each beaker:
1. For the first beaker:
\[ a = 250k = 250 \times \frac{341}{600} = \frac{85250}{600} = 142.0833 \text{ ml} \]
2. For the second beaker:
\[ b = 650k = 650 \times \frac{341}{600} = \frac{221650}{600} = 369.4167 \text{ ml} \]
3. For the third beaker:
\[ c = 300k = 300 \times \frac{341}{600} = \frac{102300}{600} = 170.5 \text{ ml} \]

### Step 8: Identify the volume filled in the largest beaker
The largest beaker is the second one with a capacity of 650 ml. The volume filled in the largest beaker is:
\[ b = 369.4167 \text{ ml} \]

### Final Answer
The volume filled in the largest beaker is approximately **369.42 ml**.

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