Mixtures and Alligations  Quant/Math  CAT 2008
Question 4 the day:
August 19, 2002
The question for the day is from the topic of Mixtures and Alligations.
 A merchant mixes three varieties 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
kgs of the second variety will be in the mixture if 2 kgs of the third
variety is there in the mixture?
(1) 
1 kg 

(2) 
5 kgs 

(3) 
3 kgs 

(4) 
6 kgs 
Correct Answer  (2)
Solution:
If the selling price of mixture is Rs.30/kg and the merchant makes a profit of
20%, then the cost price of the mixture =
30/1.2
= Rs.25/kg.
We need to find out the ratio in which the three varieties are mixed to obtain a
mixture costing Rs.25 /kg.
Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost
Rs.30/kg. The mean desired price falls between B and C.
Step 1: Find out the ratio QA : QC using alligation rule. Qa /
Qc = 3025 / 2520 =1/1
Step 2: Find out the ratio QB : QC using alligation rule.
Qb / Qc = 3025 / 2524 =5/1
Step 3: QC is found by adding the value of QC in step 1 and step 2 = 1 +
1 = 2
Therefore, the required ratio = 1 : 5 : 2
If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs
of the second variety in the mixture.
Note: This is a problem to be skipped, at least in the first go. If you
were able to solve at least 30 other problems in quant, then you should look at
this problem.