A jar contains a blend of a fruit juice and water in the ratio `15: x`. When 4 litre of water is added to 16 litres of the blend then ratio of fruit juice to water becomes `1 : 1`. What is the value of `x`?

Options

A. 9
B. 8
C. 6
D. 10

Answer

To solve the problem, we need to find the value of \( x \) in the ratio of fruit juice to water in a jar. Here’s a step-by-step solution:

### Step 1: Understand the Initial Ratio
The initial ratio of fruit juice to water is given as \( 15 : x \). This means for every 15 parts of fruit juice, there are \( x \) parts of water.

### Step 2: Calculate the Amounts in the Blend
The total blend is 16 liters. The amount of fruit juice in the blend can be calculated as:
\[ \text{Amount of fruit juice} = \frac{15}{15 + x} \times 16 \]
The amount of water in the blend can be calculated as:
\[ \text{Amount of water} = \frac{x}{15 + x} \times 16 \]

### Step 3: Add Water and Set Up the Equation
When 4 liters of water is added to the 16 liters of blend, the new amount of water becomes:
\[ \text{New amount of water} = \frac{x}{15 + x} \times 16 + 4 \]
According to the problem, the new ratio of fruit juice to water becomes \( 1 : 1 \). Therefore, we can set up the equation:
\[ \frac{240}{15 + x} = \frac{16x}{15 + x} + 4 \]
where \( 240 \) is the amount of fruit juice calculated from the previous step.

### Step 4: Clear the Denominator
Multiply both sides by \( (15 + x) \) to eliminate the fraction:
\[ 240 = 16x + 4(15 + x) \]

### Step 5: Simplify the Equation
Expanding the right side gives:
\[ 240 = 16x + 60 + 4x \]
Combining like terms results in:
\[ 240 = 20x + 60 \]

### Step 6: Solve for \( x \)
Subtract 60 from both sides:
\[ 240 - 60 = 20x \]
\[ 180 = 20x \]
Now, divide both sides by 20:
\[ x = \frac{180}{20} = 9 \]

### Conclusion
The value of \( x \) is \( 9 \).

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