A shopkeeper mixes two types of rice, one costing ₹75 per kg and the other…
2026
A shopkeeper mixes two types of rice, one costing ₹75 per kg and the other costing ₹85 per kg in the ratio 5 : 3. What is the average price per kg of the mixture?
Answer: A. ₹78.75 — ConceptWhen quantities have different unit values, the mixture's unit value is their weighted average. Weighted average = sum of (unit value × quantity…
- A.
₹78.75
- B.
₹83.76
- C.
₹80.58
- D.
₹76.25
Attempted by 45 students.
Show answer & explanation
Correct answer: A
Concept
When quantities have different unit values, the mixture's unit value is their weighted average.
Weighted average = sum of (unit value × quantity weight) ÷ sum of quantity weights.
Application
Let the quantities of the two types be 5k kg and 3k kg.
Total cost = ₹75 × 5k + ₹85 × 3k = ₹375k + ₹255k = ₹630k.
Total quantity = 5k + 3k = 8k kg.
Average price = ₹630k ÷ 8k = ₹78.75 per kg.
Cross-check
A weighted average must lie between ₹75 and ₹85 and be closer to ₹75 because the larger share has that price. Here ₹78.75 is ₹3.75 above ₹75 and ₹6.25 below ₹85; the distance ratio 3.75 : 6.25 = 3 : 5 is inverse to the quantity ratio 5 : 3, confirming the result.
Therefore, the mixture costs ₹78.75 per kg.