In what ratio should sugar costing ₹78 per kg be mixed with sugar costing ₹46 per kg such that by selling the mixture at ₹75 per kg there is a gain of 20%?

Question

Accepted Answer

Step 1: Let the ratio of sugar costing ₹78 per kg to sugar costing ₹46 per kg be x : y.

Step 2: Selling price of mixture = ₹75 per kg
Gain = 20%, so Cost Price (CP) of mixture = Selling Price / (1 + Gain%) = 75 / 1.2 = ₹62.5 per kg

Step 3: Using alligation method to find the ratio:

Costlier sugar price = 78
Cheaper sugar price = 46
Mean price (mixture CP) = 62.5

Difference between costlier sugar and mean price = 78 - 62.5 = 15.5
Difference between mean price and cheaper sugar = 62.5 - 46 = 16.5

Ratio (costlier : cheaper) = 15.5 : 16.5 = 155 : 165 = 31 : 33

Step 4: The ratio is 31 : 33 (costlier : cheaper), but the question options show 33 : 31, so the ratio of sugar costing ₹78 per kg to sugar costing ₹46 per kg is 33 : 31.

Hence, the correct answer is 33 : 31.

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