One grain is sold for ₹84/kg at 20% profit. Another is sold for ₹72/kg at 20% profit. Mixed in ratio 3:2 and sold at ₹78/kg, what is the profit/loss percentage?

Correct Answer: 18.18% profit

Step-by-Step Explanation:

To find the overall profit or loss percentage when the two grains are mixed and sold, we need to calculate the total cost price (CP) per kg of the mixture and compare it with the selling price (SP) per kg of the mixture.

Step 1: Calculate the Cost Price (CP) of each grain type per kg.

For the first grain:
Selling Price (SP₁) = ₹84/kg
Profit Percentage = 20%

Using the formula: $\text{CP}=\frac{\text{SP}}{1+\frac{\text{Profit \%}}{100}}$

${\text{CP}}_1=\frac{84}{1+0.20}=\frac{84}{1.2}=\text{₹70/kg}$

For the second grain:
Selling Price (SP₂) = ₹72/kg
Profit Percentage = 20%

${\text{CP}}_2=\frac{72}{1+0.20}=\frac{72}{1.2}=\text{₹60/kg}$

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

The two grains are mixed in the ratio 3 : 2. Let us assume we mix 3 kg of the first grain with 2 kg of the second grain (total 5 kg of mixture).

Total cost for 5 kg mixture:
$\text{Total CP}=(3\times 70)+(2\times 60)=210+120=\text{₹330}$

Cost Price per kg of the mixture:
${\text{CP}}_{\text{mixture}}=\frac{330}{5}=\text{₹66/kg}$

Step 3: Calculate the overall Profit Percentage.

Selling Price of the mixture (SP_mixture) = ₹78/kg
Since SP_mixture (₹78) > CP_mixture (₹66), there is a profit.

$\text{Profit per kg}=78-66=\text{₹12/kg}$

Profit Percentage:
$\text{Profit \%}=\left(\frac{12}{66}\right)\times 100=\left(\frac{2}{11}\right)\times 100=\frac{200}{11}\approx 18.18\%$

Hence, there is an 18.18% profit on the mixture.