In 250 litres mixture of soda and water the ratio of amount of soda to that of water is `7 : 18`. In order to make this ratio `2 : 3`, how many more litres of soda should be added ?

Options

A. 37.5
B. 42.5
C. 45
D. 50

Answer

To solve the problem step by step, we will first determine the current amounts of soda and water in the mixture, and then find out how much more soda needs to be added to achieve the desired ratio.

### Step 1: Determine the current amounts of soda and water
The given ratio of soda to water is 7:18. The total volume of the mixture is 250 liters.

To find the amount of soda and water, we first calculate the total parts in the ratio:
\[ \text{Total parts} = 7 + 18 = 25 \]

Now, we can find the amount of soda and water:
\[ \text{Amount of soda} = \left(\frac{7}{25}\right) \times 250 = 70 \text{ liters} \]
\[ \text{Amount of water} = \left(\frac{18}{25}\right) \times 250 = 180 \text{ liters} \]

### Step 2: Set up the equation for the new ratio
We want to change the ratio of soda to water to 2:3. Let \( x \) be the amount of soda we need to add.

After adding \( x \) liters of soda, the new amount of soda will be:
\[ 70 + x \text{ liters} \]
The amount of water remains the same at 180 liters.

The new ratio of soda to water can be expressed as:
\[ \frac{70 + x}{180} = \frac{2}{3} \]

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 3(70 + x) = 2 \times 180 \]
Expanding both sides:
\[ 210 + 3x = 360 \]

### Step 4: Solve for \( x \)
Now, isolate \( x \):
\[ 3x = 360 - 210 \]
\[ 3x = 150 \]
\[ x = \frac{150}{3} = 50 \]

### Conclusion
To achieve the desired ratio of 2:3, we need to add **50 liters of soda** to the mixture.

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