Two types of sugar, one costing ₹45/kg and another costing ₹60/kg, are mixed with a third variety in the ratio 1:2:3. If the mixture is worth ₹55/kg, what is the price of the third variety of sugar per kg?
₹55.00
Let the price of the third variety be \(x\) per kg. Using the weighted-average price of the mixture:
\(\dfrac{1 \times 45 + 2 \times 60 + 3 \times x}{1 + 2 + 3} = 55\)
\(\dfrac{45 + 120 + 3x}{6} = 55\)
\(165 + 3x = 330 \implies 3x = 165 \implies x = 55\)
Hence the price of the third variety is ₹55.00 per kg.
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Important Questions from Mixture and Alligation
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- Pure ghee costs ₹112/kg. After adulterating it with vegetable oil costing ₹56/kg, a dishonest shopkeeper sells the mixture at the rate of ₹91/kg, thereby making a profit of 30%. In what ratio does he mix the two?
- Container A contains $30$ litres of pure milk costing $₹40$ per litre, and container B contains $50$ litres of pure milk costing $₹50$ per litre. The entire contents are mixed together. By how much is the average cost per litre of the mixture more or less than the average cost per litre of container A's milk?
- Pure ghee costs $₹86/kg$. After adulterating it with vegetable oil costing $₹43/kg$, a dishonest shopkeeper sells the mixture at the rate of $₹80/kg$, thereby making a profit of $60\%$. In what ratio does he mix the two?
