A baker buys three types of flour: wheat, rye, and oats. Wheat flour costs 5 for ₹40, rye flour at 6 for ₹45, and oats flour at 4 for ₹36. He mixes them in the ratio 2:2:3. He sells all the mixed flour at 3 for ₹32. What is his approximate profit or loss percentage?

Correct Option: Profit of 29%

Step-by-Step Explanation:

Step 1: Find the cost price per unit for each type of flour.

Cost price per unit of wheat flour = ₹40 ÷ 5 = ₹8
Cost price per unit of rye flour = ₹45 ÷ 6 = ₹7.5
Cost price per unit of oats flour = ₹36 ÷ 4 = ₹9

Step 2: Calculate the total Cost Price (CP) of the mixture.

The baker mixes wheat, rye, and oats flour in the ratio 2 : 2 : 3.

Let the quantities mixed be 2 units, 2 units, and 3 units respectively.

Total quantity of the mixture = 2 + 2 + 3 = 7 units.

Now, calculate the total cost price of these 7 units:

Total CP = (2 × ₹8) + (2 × ₹7.5) + (3 × ₹9)

Total CP = ₹16 + ₹15 + ₹27 = ₹58

Step 3: Calculate the total Selling Price (SP) of the mixture.

The selling rate is 3 units for ₹32, which means the selling price per unit is ₹32 ÷ 3.

For the total 7 units of the mixture:

$\text{Total SP}=7\times \frac{32}{3}=\frac{224}{3}\text{ ₹}$

Step 4: Calculate the Profit and Profit Percentage.

Since the total Selling Price is greater than the total Cost Price, there is a profit.

$\text{Profit}=\text{Total SP}-\text{Total CP}$

$\text{Profit}=\frac{224}{3}-58=\frac{224-174}{3}=\frac{50}{3}\text{ ₹}$

Now, calculate the approximate profit percentage:

$\text{Profit \%}=\left(\frac{\text{Profit}}{\text{Total CP}}\right)\times 100$

$\text{Profit \%}=\left(\frac{50/3}{58}\right)\times 100=\frac{50}{3\times 58}\times 100=\frac{5000}{174}\approx 28.735\%$

Rounding off to the nearest whole percentage, we get approximately 29% Profit.