Answer :
Final answer:
The quantity of loose sugar that needs to be mixed with 126 kg of Madhur sugar, in order to gain a 20% profit when sold at Rs. 48 per kg, is 63 kg.
Explanation:
The problem involves a concept called mixture problems in mathematics. Here, we are asked to find the quantity (in KG) of loose sugar costing Rs. 34 per kg which needs to be mixed with 126 kg of Madhur sugar priced at Rs. 42 per kg to gain a 20% profit when sold at Rs. 48 per kg.
Let's consider the quantity of loose sugar to be mixed as 'x' kg. To have 20% profit, the cost price (CP) of the mixture should be Rs. 48/1.2 = Rs. 40 per kg. Thus, we can form the equation for the total cost price of the mixture as:
34x (cost of loose sugar) + 42*126 (cost of Madhur sugar) = 40 * (x+126) (cost price of total mixture)
Solving this equation, we will get x = 63 Kg. Hence, 63 Kg of loose sugar must be mixed with 126 Kg of Madhur sugar to gain the desired profit.
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Final answer:
To find the quantity of loose sugar to be mixed with 126kg of Madhur sugar, we use the mixture rule, assuming the cost price for the sugar mixture to be Rs.40/kg (since the selling price is Rs.48/kg for a 20% profit). Solving gives us a result of approximately 315 kg for the cheaper quantity of sugar.
Explanation:
To solve this problem, we've to find a point of equilibrium in the mixture in terms of sugar prices and quantity. The student wants to gain a 20% profit by selling the mixture at Rs.48 per kg. That means the cost price of the mixture will be 48/1.20 = Rs.40 per kg.
Now, we find the quantity of loose sugar to be mixed with Madhur sugar so that the mixture costs Rs.40 per kg. For this, we use the rule of mixture which states: (Cheaper Quantity / Dearer Quantity) = ((Dearer Price - Mean Price) / (Mean Price - Cheaper Price)).
- Cheaper Price: Rs.34/kg
- Dearer Price: Rs.42/kg
- Mean Price: Rs.40/kg
Substituting the values, we get our answer: (Cheaper Quantity / 126) = (42 - 40) / (40 - 34).
Solving for Cheaper Quantity yields approximately 315 kg.
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