In what ratio should two varieties of sugar at Rs.18 per kg and Rs.24 Kg be mixed together to get a mixture whose cost is Rs.20 per kg?

We are asked to find the ratio in which two varieties of sugar, costing Rs. 18 per kg and Rs. 24 per kg, should be mixed to get a mixture that costs Rs. 20 per kg. Here's the step-by-step approach:

1. Let the quantities of the two varieties of sugar be:
   • Let the quantity of sugar at Rs. 18 per kg be x kg.
   • Let the quantity of sugar at Rs. 24 per kg be y kg.
2. Cost equation for the mixture:
   • The total cost of the sugar mixture is the sum of the costs of the two varieties of sugar.
   • The cost of the sugar at Rs. 18 per kg is 18x and the cost of the sugar at Rs. 24 per kg is 24y.
   • The total weight of the mixture is x + y kg, and we want the cost of the mixture to be Rs. 20 per kg.
   • The total cost of the mixture should be 20(x + y) rupees.

   Thus, the cost equation becomes:

   18x + 24y = 20(x + y)
3. Simplify the equation:
   • Expanding the equation: 18x + 24y = 20x + 20y
   • Now, bring like terms together: 18x - 20x = 20y - 24y
   • This simplifies to: -2x = -4y
   • Dividing both sides by -2: x = 2y
4. Conclusion:
   • The ratio of x to y is x/y = 2/1.
   • Therefore, the two varieties of sugar should be mixed in the ratio of 2:1.
5. Final answer:

   The two varieties of sugar should be mixed in the ratio 2:1.