Ramesh bought two varieties of rice costing 45 Rs per kg and 55 Rs per kg and…
2025
Ramesh bought two varieties of rice costing 45 Rs per kg and 55 Rs per kg and mixed them in some ratio. Then he sold that mixture at 60 Rs per kg, making a profit of 20%. What was the ratio of the mixture?
Answer: D. 1:1 — Concept: When a selling price (SP) is achieved at a profit of p%, the cost price is CP = SP ÷ (1 + p/100). When two ingredients priced c1 and c2 per unit are…
- A.
2:3
- B.
1:4
- C.
2:5
- D.
1:1
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Correct answer: D
Concept: When a selling price (SP) is achieved at a profit of p%, the cost price is CP = SP ÷ (1 + p/100). When two ingredients priced c1 and c2 per unit are mixed to give a mixture at a mean price m, the alligation rule gives the ratio of their quantities as (quantity at c1) : (quantity at c2) = (c2 − m) : (m − c1).
Application: Applying the rule to this problem:
Find the required cost price of the mixture: CP = 60 ÷ (1 + 20/100) = 60 ÷ 1.2 = 50 Rs/kg.
Apply the alligation rule with c1 = 45, c2 = 55, and m = 50: ratio = (55 − 50) : (50 − 45) = 5 : 5 = 1 : 1.
So Ramesh must mix the two varieties of rice in equal quantities.
Cross-check: Taking 1 kg of each variety, the weighted average cost is (45 × 1 + 55 × 1) ÷ (1 + 1) = 100 ÷ 2 = 50 Rs/kg, which matches the required cost price of 50 Rs/kg — confirming the 1:1 ratio.
Answer: The mixture ratio is 1:1.