Sugar at Rs. 15 per kg is mixed with sugar at Rs. 20 per kg in the ratio 2 : 3 Find the price per kg of the mixture -----

Options

A. Rs. 18
B. Rs.16
C. Rs.17
D. Rs.19

Answer

To find the price per kg of the mixture of two types of sugar, we can use the concept of alligation. Here’s a step-by-step solution:

### Step 1: Identify the costs and the ratio
We have:
- Cost of sugar 1 (C1) = Rs. 15 per kg
- Cost of sugar 2 (C2) = Rs. 20 per kg
- Ratio of mixing (R1:R2) = 2:3

### Step 2: Set up the alligation formula
We need to find the price per kg of the mixture (Z). According to the alligation rule, we can set up the following equation:

\[ \frac{C2 - Z}{Z - C1} = \frac{R1}{R2} \]

Substituting the known values:

\[ \frac{20 - Z}{Z - 15} = \frac{2}{3} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:

\[ 3(20 - Z) = 2(Z - 15) \]

### Step 4: Distribute and simplify
Distributing both sides:

\[ 60 - 3Z = 2Z - 30 \]

### Step 5: Rearrange the equation
Now, rearranging the equation to get all Z terms on one side:

\[ 60 + 30 = 2Z + 3Z \]

This simplifies to:

\[ 90 = 5Z \]

### Step 6: Solve for Z
Now, divide both sides by 5 to find Z:

\[ Z = \frac{90}{5} = 18 \]

### Step 7: Conclusion
The price per kg of the mixture is Rs. 18.

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