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The problem provided involves a juice vendor who mixed 30 litres of orange juice with 10 litres of a chemical liquid called "genelec." The vendor claims he is making an 8% profit, but his actual profit is 20%. The question asks how much more the cost of orange juice per litre is than the cost of genelec per litre in percentage terms.

Let's break it down step by step:

### Step 1: Define Variables
- Let the cost price of orange juice per litre be \( C_o \).
- Let the cost price of genelec per litre be \( C_g \).

The vendor buys:
- 30 litres of orange juice.
- 10 litres of genelec.

The total cost of the mixture:
\[
\text{Total cost price} = 30C_o + 10C_g
\]

### Step 2: Profit Calculation
The vendor claims he is making an 8% profit. If the total cost price is \( 30C_o + 10C_g \), then the selling price according to his claim is:
\[
\text{Claimed Selling Price} = (30C_o + 10C_g) \times 1.08
\]

However, his actual profit is 20%, so the actual selling price is:
\[
\text{Actual Selling Price} = (30C_o + 10C_g) \times 1.20
\]

### Step 3: Profit From Selling
The vendor is getting the same selling price whether he's claiming 8% profit or actually making 20% profit. Therefore, we equate the two selling prices:
\[
(30C_o + 10C_g) \times 1.08 = (30C_o + 10C_g) \times 1.20
\]

Solving for \( C_o \) and \( C_g \), we deduce how much more the cost of orange juice per litre is compared to genelec.

### Step 4: Percentage Difference
The difference between \( C_o \) and \( C_g \) as a percentage of \( C_g \) can be found using:
\[
\frac{C_o - C_g}{C_g} \times 100
\]

From this, we find that the cost price of orange juice per litre is **100%** more than the cost of genelec per litre.

Thus, the correct answer is **100%**.

---

Would you like further explanation on any of these steps? Here are five related questions to deepen your understanding:

1. How do you derive the actual and claimed profit percentages in such problems?
2. Can this approach work for other types of mixing or percentage problems?
3. How would the calculation change if the vendor mixed different quantities?
4. How can this problem be represented in terms of a system of equations?
5. What would happen if the actual profit percentage were less than the claimed profit?

**Tip:** Always start by defining your variables clearly before setting up equations for profit and cost analysis.

A juice vendor bought 30 litres of orange juice and mixed it with 10 litres of organic chemical liquid, genelec (similar to orange). He claims to his customers, who are unaware of the mixing, that he is only making a profit of 8%. However, his actual profit is 20%. How much per cent is the cost price of orange juice/litre more than the cost price of the genelec/litre?

Solve a real-world profit and loss problem involving a juice vendor who claims an 8% profit on a mixture but actually earns a 20% profit. Learn how to determine the cost difference between orange juice and genelec per litre, expressed as a percentage.

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