5 kg of superior quality of sugar is mixed with 25 kg of inferior quality sugar. The price of superior quality and inferics quality sugar is Rs. 18 and Rs. 12 respectively. The average price per kg of the mixture is :

Options

A. Rs. 13
B. Rs. 15
C. Rs. 18
D. Rs. 21

Answer

To find the average price per kg of the mixture of sugar, we can follow these steps:

### Step 1: Calculate the total cost of superior quality sugar
- The quantity of superior quality sugar = 5 kg
- The price per kg of superior quality sugar = Rs. 18

**Total cost of superior quality sugar = Quantity × Price per kg**
\[ \text{Total cost of superior quality sugar} = 5 \, \text{kg} \times 18 \, \text{Rs/kg} = 90 \, \text{Rs} \]

### Step 2: Calculate the total cost of inferior quality sugar
- The quantity of inferior quality sugar = 25 kg
- The price per kg of inferior quality sugar = Rs. 12

**Total cost of inferior quality sugar = Quantity × Price per kg**
\[ \text{Total cost of inferior quality sugar} = 25 \, \text{kg} \times 12 \, \text{Rs/kg} = 300 \, \text{Rs} \]

### Step 3: Calculate the total cost of the mixture
**Total cost of the mixture = Total cost of superior quality sugar + Total cost of inferior quality sugar**
\[ \text{Total cost of the mixture} = 90 \, \text{Rs} + 300 \, \text{Rs} = 390 \, \text{Rs} \]

### Step 4: Calculate the total quantity of the mixture
**Total quantity of the mixture = Quantity of superior quality sugar + Quantity of inferior quality sugar**
\[ \text{Total quantity of the mixture} = 5 \, \text{kg} + 25 \, \text{kg} = 30 \, \text{kg} \]

### Step 5: Calculate the average price per kg of the mixture
**Average price per kg = Total cost of the mixture / Total quantity of the mixture**
\[ \text{Average price per kg} = \frac{390 \, \text{Rs}}{30 \, \text{kg}} = 13 \, \text{Rs/kg} \]

Thus, the average price per kg of the mixture is **Rs. 13**.

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