Multiple choice

A shopkeeper mixed $10$ kg of rice costing Rs. $10$ per kg with a certain quantity of another variety of rice costing Rs. $15$ per kg. He sold the mixture at the rate of Rs. $14$ per kg. What was the quantity of the second variety of rice, if he gained by $5$ $\% $?

  1. $20$ kg
  2. $18$ kg
  3. $33$ kg
  4. $45$ kg
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A Correct answer
Explanation

Let x be the quantity of the second rice. Total cost = 10*10 + 15*x = 100 + 15x. Total weight = 10 + x. Selling price = 14(10 + x). Gain is 5%, so 1.05 * (100 + 15x) = 14(10 + x). Solving for x gives 105 + 15.75x = 140 + 14x, so 1.75x = 35, x = 20.

AI explanation

The selling price is Rs. 14 per kg, which includes a 5% gain, so the cost price of the mixture is 14 divided by 1.05, yielding Rs. 40/3 per kg. Using the rule of alligation, the ratio of the Rs. 10 rice to the Rs. 15 rice is (15 - 40/3) : (40/3 - 10), which simplifies to 5/3 : 10/3, or 1 : 2. If 10 kg is one part, the quantity of the second variety is 2 parts, which equals 20 kg.

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