# Mixtures & Alligation: Mixture of 3 Variants

This aptitude practice question is a mixtures and alligation question. Concept tested: Finding ratio of mixture of 3 variants using rule of alligation.

## Question

A merchant mixes three variants of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30/kg. How many kg of the second variant will be in the mixture if 2 kgs of the third variant is there in the mixture?

1. 1 kg
2. 5 kgs
3. 3 kgs
4. 6 kgs

Correct Answer      Choice (2). 5 kgs

Step 1: 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 = $$frac{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. Step 2.1: Find out the ratio QA : QC using alligation rule. $\frac{{Q}_{A}}{{Q}_{C}}$ = $\frac{30-25}{25-20}$ = $\frac{1}{1}$ = 1 : 1 Step 2.2: Find out the ratio QB : QC using alligation rule. $\frac{{Q}_{B}}{{Q}_{C}}$ = $\frac{30-25}{25-24}$ = $\frac{5}{1}$ = 5 : 1 Step 2.3: QC is common to both the ratios. The value of QC is found by adding the value of QC in step 2.1 and step 2.2 = 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. Note: This question is a time consuming question. If you can revisit questions in the test, mark it for review and proceed to the next one. Else, skip this question without batting an eyelid. The correct answer is Choice$2).

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