Multiple choice

How many kilograms of rice of Rs.5.4 per kg should be mixed with 10 kg of rice of Rs.4.5 per kg, such that there may be gain of 20% by selling the mixture at Rs.5.94 per kg.

  1. 10 kg

  2. 12 kg

  3. 15 kg

  4. 8 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the quantity of rice at Rs. 5.4/kg. The cost price of the mixture is (5.4x + 4.5*10) / (x + 10). To gain 20% at a selling price of 5.94, the cost price must be 5.94 / 1.2 = 4.95. Solving (5.4x + 45) / (x + 10) = 4.95 yields 5.4x + 45 = 4.95x + 49.5, so 0.45x = 4.5, giving x = 10 kg.

AI explanation

To achieve a 20% gain on cost by selling at Rs. 5.94 per kg, the cost price of the mixture must be 5.94 / 1.20, which equals Rs. 4.95 per kg. Using the method of alligation with the Rs. 5.40 rice and the Rs. 4.50 rice, the ratio is (4.95 - 4.50) : (5.40 - 4.95), giving 0.45 : 0.45 or 1 : 1. Since the second type is 10 kg, the first type must also be 10 kg.

Keep practicing — related questions