In what ratio must a grocer mix two varieties of pulses costing ₹105 per kg…
2026
In what ratio must a grocer mix two varieties of pulses costing ₹105 per kg and ₹120 per kg, respectively, to obtain a mixture worth ₹106.50 per kg?
Answer: C. 9 : 1 — ConceptWhen two ingredients with lower and higher unit costs are mixed to obtain a mean cost between them, the alligation rule gives their quantity ratio as:…
- A.
5 : 1
- B.
7 : 1
- C.
9 : 1
- D.
1 : 5
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Correct answer: C
Concept
When two ingredients with lower and higher unit costs are mixed to obtain a mean cost between them, the alligation rule gives their quantity ratio as:
quantity at lower cost : quantity at higher cost = (higher cost − mean cost) : (mean cost − lower cost).
Application
Let the required quantities of the pulses costing ₹105 per kg and ₹120 per kg be x kg and y kg, respectively.
Substitute the costs in the alligation ratio: x : y = (120 − 106.50) : (106.50 − 105).
Compute the differences: x : y = 13.50 : 1.50.
Divide both terms by 1.50: x : y = 9 : 1.
Cross-check
For 9 kg of the ₹105 pulse and 1 kg of the ₹120 pulse, the average cost is (9 × 105 + 1 × 120) ÷ (9 + 1) = (945 + 120) ÷ 10 = ₹106.50 per kg.
Therefore, the required ratio is 9 : 1.