A merchant mixes three variants of rice costing Rs 20 kg Rs 24 kg and Rs 30 kg and sells the mixture...........

Explanation:

Compute cost price of 1 kg of mixture.
The selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%.
If the cost of 1 kg of the mixture is c, c + 20% of c = 1.2 c = selling price
The cost price of the mixture, c = 30/1.2 = Rs.25/kg.

Step 2: Find the ratio in which the 3 variants are mixed
The three variants are mixed to obtain a mixture that costs Rs.25 /kg.
Variant A costs Rs.20/kg, variant B costs Rs.24/kg and variant C costs Rs.30/kg.

The mean price of the mixture falls between the costs of B and C.

Find out the ratio QA : QC using alligation rule. QA/QC = 30−25/25−20 = 1/1 = 1 : 1
Find out the ratio QB : QC using alligation rule. QB/QC = 30−25/25−24 = 5/1 = 5 : 1
QC is common to both the ratios. The value of QC is found by adding the value of QC = 1 + 1 = 2
Therefore, the required ratio = 1 : 5 : 2
If there are 2 kgs of the third variant in the mixture, then there will be 5 kgs of the second variant in the mixture.

Hence, option 2 is the correct answer.