test tube contains a certain solution of water, soap and sugar. The ratio of water to soap is 2:1 and the ratio of soap to sugar is 2 times
Ops:
this ratio. The solution is transferred in a pan and heated up. After some timeteh ratio of water to soap in the pan is now reduced to one third by water evaporation. What will be the ratio of water to sugar now?
A.
02:1
B.
O 12:3
C. O3:1 D.
08:3

Let's break down the problem step by step:

### Step 1: Initial Ratios in the Test Tube
- The ratio of **water to soap** is given as **2:1**.
- The ratio of **soap to sugar** is **twice** the water-to-soap ratio. Hence, the ratio of soap to sugar will be **2 × 2 = 4:1**.

Now, let's represent these ratios in terms of variables:
- Let the amount of **soap** be \( s \).
- The amount of **water** will then be \( 2s \) (since the ratio of water to soap is 2:1).
- The amount of **sugar** will be \( \frac{s}{4} \) (since the ratio of soap to sugar is 4:1).

So initially:
- Water = \( 2s \)
- Soap = \( s \)
- Sugar = \( \frac{s}{4} \)

### Step 2: After Water Evaporation in the Pan
- After heating, the ratio of **water to soap** is reduced to **one-third** of its original value. Originally, the water-to-soap ratio was 2:1. One-third of this ratio is \( \frac{2}{3}:1 \).
  
This means that now:
- New amount of **water** = \( \frac{2}{3} \times \text{soap} = \frac{2}{3}s \).
  
So, after the evaporation:
- Water = \( \frac{2}{3}s \)
- Soap = \( s \) (remains the same)
- Sugar = \( \frac{s}{4} \) (remains the same)

### Step 3: Find the New Ratio of Water to Sugar
Now, the new ratio of **water to sugar** is:
\[
\text{Water to sugar} = \frac{\frac{2}{3}s}{\frac{s}{4}} = \frac{2}{3} \times \frac{4}{s} = \frac{8}{3}.
\]

Thus, the new ratio of water to sugar is \( 8:3 \).

### Final Answer:
The correct option is **D. 8:3**.

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Do you need any further clarification or details? Here are some follow-up questions you can explore:

1. What would happen to the ratio if more water evaporated from the solution?
2. How can the ratios of different components affect the properties of a solution?
3. If the ratio of soap to sugar were different initially, how would that change the final ratio?
4. How would the mass of the solution change as water evaporates?
5. Can you find another method to verify the final ratio of water to sugar?

**Tip:** Ratios are always relative and remain proportional, even when the total amount of one component changes significantly.

A test tube contains a certain solution of water, soap, and sugar. The ratio of water to soap is 2:1, and the ratio of soap to sugar is 2 times this ratio. The solution is transferred to a pan and heated up. After some time, the ratio of water to soap in the pan is reduced to one-third due to water evaporation. What will be the ratio of water to sugar now? Options: A. 2:1 B. 12:3 C. 3:1 D. 8:3

Explore how to calculate the new ratio of water to sugar after water evaporates from a solution. This math problem uses the concept of ratios and proportions, covering key algebraic steps. Ideal for students in Grades 8-10.

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