Question

Three varieties of rice costing ₹40/kg, ₹50/kg, and a third unknown price are mixed in the ratio 2:3:5. If the resulting mixture is sold at ₹55/kg, making a profit of 10% on the cost price, what is the price of the third variety of rice per kg?

• A. ₹52.50
• B. ₹57.50
• C. ₹54.00
• D. ₹62.50

Answer 1

Answer:

C. ₹54.00

Let the price of the third variety be ₹(x) per kg.

Step 1: Find cost price of mixture

Selling price = ₹55/kg and profit = 10%

So cost price (CP) of mixture:

$CP = \frac{55}{1.1} = 50$

So, the mixture costs ₹50/kg.

Use weighted average

Mixture ratio = (2:3:5)

So average cost price:

$\frac{2(40) + 3(50) + 5(x)}{2+3+5} = 50$

$\frac{80 + 150 + 5x}{10} = 50$

230 + 5x = 500

5x = 270

x = 54

=₹54.00