Sugar Mixture Ratio Calculation
This problem requires finding the ratio to mix two types of sugar (Quality A and Quality B) to achieve a specific mixture cost. First, we determine the cost per kg for each quality, then use the principle of alligation.
Calculate Cost Per Kilogram for Each Sugar Quality
Quality A Sugar Cost:
- Given: 7 kg costs ₹245.
- Cost per kg (A) = \(\frac{₹245}{7 \text{ kg}} = ₹35 \text{ per kg}\).
Quality B Sugar Cost:
- Given: 5 kg costs ₹300.
- Cost per kg (B) = \(\frac{₹300}{5 \text{ kg}} = ₹60 \text{ per kg}\).
Apply the Rule of Alligation
Alligation is used to find the ratio of quantities when mixing two items of different prices to obtain a mixture at a specific mean price.
- Cost of Quality A (Cheaper) = ₹35/kg
- Cost of Quality B (Dearer) = ₹60/kg
- Desired Mixture Cost (Mean Price) = ₹50/kg
The ratio of the quantities is determined by the differences between the costs:
Ratio of Quality A : Quality B = (Cost of B - Mixture Cost) : (Mixture Cost - Cost of A)
Ratio \(A : B = (₹60 - ₹50) : (₹50 - ₹35)\)
Ratio \(A : B = 10 : 15\)
Simplify the Ratio
Divide both parts of the ratio by their greatest common divisor (5):
Simplified Ratio \(A : B = \frac{10}{5} : \frac{15}{5} = 2 : 3\).
Thus, Quality A and Quality B sugar should be mixed in the ratio 2:3.
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Important Questions from Mixture and Alligation
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If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?
A vessel full of water weighs 4o kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?
