A mixed grain flour is made by mixing 2 parts of mixed grains and three parts of wheat flour. If the mixed grains cost Rs 40 per kg and wheat costs Rs 30 per kg, find at what price the mixed grain flour needs to be sold to make a profit of `10%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the parts of the mixture
The mixed grain flour is made by mixing 2 parts of mixed grains and 3 parts of wheat flour. Therefore, the total parts of the mixture is:
\[ \text{Total parts} = 2 + 3 = 5 \text{ parts} \]

### Step 2: Calculate the weight of each component in 1 kg of mixed grain flour
Since we are considering 1 kg (1000 grams) of mixed grain flour:
- Weight of mixed grains = \( \frac{2}{5} \times 1000 \text{ grams} = 400 \text{ grams} \)
- Weight of wheat flour = \( \frac{3}{5} \times 1000 \text{ grams} = 600 \text{ grams} \)

### Step 3: Calculate the cost of mixed grains
The cost of mixed grains is Rs. 40 per kg. Therefore, the cost for 400 grams is:
\[ \text{Cost of mixed grains} = 40 \text{ Rs/kg} \times \frac{400 \text{ grams}}{1000 \text{ grams}} = 40 \times 0.4 = 16 \text{ Rs} \]

### Step 4: Calculate the cost of wheat flour
The cost of wheat flour is Rs. 30 per kg. Therefore, the cost for 600 grams is:
\[ \text{Cost of wheat flour} = 30 \text{ Rs/kg} \times \frac{600 \text{ grams}}{1000 \text{ grams}} = 30 \times 0.6 = 18 \text{ Rs} \]

### Step 5: Calculate the total cost price (CP) of 1 kg of mixed grain flour
Now, we can find the total cost price by adding the costs of mixed grains and wheat flour:
\[ \text{Total CP} = \text{Cost of mixed grains} + \text{Cost of wheat flour} = 16 \text{ Rs} + 18 \text{ Rs} = 34 \text{ Rs} \]

### Step 6: Calculate the profit for a 10% profit margin
To find the selling price (SP) that includes a 10% profit, we first calculate the profit:
\[ \text{Profit} = 10\% \text{ of CP} = \frac{10}{100} \times 34 = 3.4 \text{ Rs} \]

### Step 7: Calculate the selling price (SP)
Finally, we can find the selling price by adding the profit to the cost price:
\[ \text{SP} = \text{CP} + \text{Profit} = 34 \text{ Rs} + 3.4 \text{ Rs} = 37.4 \text{ Rs} \]

### Final Answer
The mixed grain flour needs to be sold at Rs. 37.4 per kg to make a profit of 10%.

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