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:
- 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.
- 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)
- 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
- 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.
- Final answer:
The two varieties of sugar should be mixed in the ratio 2:1.
