In what ratio should a shopkeeper mix two types of rice, one costing ₹20 per kg and another costing ₹40 per kg to get a rice variety costing ₹ 28 per kg?
In what ratio should a shopkeeper mix two types of rice, one costing ₹20 per kg and another costing ₹40 per kg to get a rice variety costing ₹ 28 per kg?
Solution
A shopkeeper has two types of rice:
- Cheaper rice: ₹20 per kg
- Expensive rice: ₹40 per kg
The goal is to mix them to get rice costing ₹28 per kg.
Using the alligation method:
Cheaper Rice Mixture Expensive Rice
₹20 → ₹28 ← ₹40
Finding the differences:
Difference 1:
Difference 2:
The ratio of cheaper rice to expensive rice is obtained by cross-matching the differences:
Cheaper Rice : Expensive Rice
Simplifying by dividing both by 4:
Cheaper Rice : Expensive Rice
Checking with 3 kg of ₹20 rice and 2 kg of ₹40 rice:
Total cost
Total weight kg
Average price per kg
The shopkeeper should mix the cheaper rice (₹20 per kg) and expensive rice (₹40 per kg) in the ratio .
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