Four varieties of wheat costing ₹30/kg, ₹45/kg, ₹60/kg and an unknown price are mixed in ratio 1:2:3:4. The mixture is sold at ₹46/kg with 15% profit. What is the cost of the fourth variety?

Correct Answer: ₹25/kg

Step-by-step explanation:

Step 1: Calculate the overall Cost Price (CP) of the mixture per kg
We are given that the mixture is sold at a selling price (SP) of ₹46/kg with a profit of 15%.

The formula relating Selling Price, Cost Price, and Profit Percentage is:

$\text{Selling Price}=\text{Cost Price}\times \left(1+\frac{\text{Profit \%}}{100}\right)$

Substitute the given values into the formula:

$46=\text{Cost Price}\times \left(1+\frac{15}{100}\right)$

$46=\text{Cost Price}\times 1.15$

$\text{Cost Price}=\frac{46}{1.15}=40$

So, the weighted cost price of the wheat mixture is ₹40/kg.

Step 2: Formulate the weighted average cost equation
Let the cost of the fourth variety of wheat be ₹$x$/kg.
The four varieties cost ₹30/kg, ₹45/kg, ₹60/kg, and ₹$x$/kg respectively, and they are mixed in the ratio $1:2:3:4$.

The total number of ratio parts is:

$1+2+3+4=10$

The weighted average cost price of the mixture is given by:

$\text{Cost Price of Mixture}=\frac{(1\times 30)+(2\times 45)+(3\times 60)+(4\times x)}{10}$

Step 3: Solve for $x$
Substitute the cost price of the mixture (₹40/kg) into the equation:

$40=\frac{30+90+180+4x}{10}$

$40=\frac{300+4x}{10}$

Multiply both sides by 10:

$400=300+4x$

Subtract 300 from both sides:

$4x=100$

$x=25$

Thus, the cost of the fourth variety of wheat is ₹25/kg.