Multiple choice

The owner of a grocery shop purchases two varieties of grain. The price of the first variety is twice the price of the second one. He mixes both the varieties and sells the mixture at a price of Rs. 28 per kg, making a profit of 25%. If the ratio of the first variety of grain and the second variety of grain in the mixture is 2 : 3, find the price of the first variety of grain.

  1. Rs. 16/kg

  2. Rs. 24/kg

  3. Rs. 32/kg

  4. Rs. 64/kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let prices be 2x and x. Ratio 2:3. Average cost = (2*2x + 3*x) / 5 = 7x/5. Selling price = 28, profit 25%. Cost price = 28 / 1.25 = 22.4. 7x/5 = 22.4 => 7x = 112 => x = 16. Price of first variety = 2x = 32.

AI explanation

The selling price of Rs. 28 per kg includes a 25% profit, so by calculating the cost price we get 28 / 1.25 = Rs. 22.40 per kg. Using the rule of alligation with the ratio 2:3 (first variety to second variety), let the price of the second variety be x, making the first variety 2x. The alligation cross-difference gives the equation (2x - 22.40) / (22.40 - x) = 3 / 2, which solves to x = 16. Therefore, the first variety costs 2 * 16 = Rs. 32/kg.

Keep practicing — related questions