Questions :
Three varieties of rice costing ₹30/kg, ₹45/kg, and a third unknown price are mixed in the ratio 3 : 2 : 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?
Options :
- ₹52.50
- ₹57.50
- ₹64.00
- ₹68.50
correct answer : c)
Explanation :
SP of mixture = ₹55/kg
CP of mixture = 55 × (100/110) = ₹50/kg
Mixing ratio = 3 : 2 : 5
Let the cost price of the third variety be ₹x/kg.
So,
(3 × 30) + (2 × 45) + (5 × x) = 50 × (3 + 2 + 5)
⇒ 90 + 90 + 5x = 50 × 10
⇒ 180 + 5x = 500
⇒ 5x = 320
⇒ x = 64
Therefore, the price of the third variety of rice is ₹64 per kg.
Hence, the correct answer is option (c) ₹64.00. The options ₹52.50, ₹57.50, and ₹68.50 are incorrect because they do not satisfy the weighted average cost of ₹50/kg required for a mixture sold at ₹55/kg with a 10% profit.