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?

Concept Used: This is a classic example of the Alligation Rule, used to find the ratio in which two or more ingredients at different prices should be mixed to obtain a mixture at a given price.

Step 1: Understand the Problem

We are given:

• Cheaper variety price (C) = Rs.18/kg
• Costlier variety price (D) = Rs.24/kg
• Mean price of mixture (M) = Rs.20/kg

Step 2: Apply Alligation Formula

We apply the rule of alligation which says:

        C (cheaper)     D (dearer)
           Rs.18          Rs.24
               \          /
                \        /
               Mean Price = Rs.20
                /        \
               /          \
     D - M = 24 - 20 = 4   M - C = 20 - 18 = 2

Step 3: Calculate the Ratio

Required ratio = (D - M) : (M - C) = 4 : 2 = 2 : 1

Final Answer: 2 : 1

This means that the two varieties of sugar priced at Rs.18/kg and Rs.24/kg should be mixed in the ratio 2:1 respectively (i.e., 2 parts of Rs.18 sugar and 1 part of Rs.24 sugar).

Why It Works:

The alligation rule leverages the concept of balancing the overall average price of the mixture by proportionally adjusting the quantities of two items based on how far they deviate from the mean price. In this case, since the mean price is Rs.20, and the difference from Rs.24 is higher than from Rs.18, less of the more expensive sugar is needed to balance the cost.

Bonus Tip for Students:

This kind of problem frequently appears in banking exams, SSC, railways, and other aptitude-based competitive tests. Practicing alligation-based questions not only saves time but also strengthens your understanding of ratio, average, and mixture concepts.