Mixtures & Alligations Question Answers

Mixtures and Alligations - Quant/Math - CAT 2008

Question 4 the day: July 4, 2002

In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?

(1)

1 : 2 : 4

(2)

3 : 7 : 6

(3)

1 : 4 : 2

(4)

None of these

Correct Answer - (3)

 

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Solution:

The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96 => Cost = 96/1.2 = Rs.80 / kg.
Let the three varities be A, B, and C costing Rs.60, Rs.75 and Rs.100 respectively.
The mean price falls between B and C.

Hence the following method should be used to find the ratio in which they should be mixed.
Step 1. Find out the ratio of Q_A : Q_C using alligation rule  Qa/Qc  =  100-80  /  80-60  1/1
Step 2. Find out the ratio of Q_B : Q_C using alligation rule   Qb / Qc = 100-80/80-75  = 4/1
Step 3. Q_C, the resultant ratio of variety c can be found by adding the value of Q_C in step 1 and step 2 = 1 + 1 = 2.

However, in CAT if you try and solve the problem using the above method, you will end up spending more than 2, and may be 3 minutes on this problem, which is a criminal mismanagement of time.
The best way to solve a problem of this kind in CAT is to go from the answer choices as shown below

The resultant ratio Q_A : Q_B : Q_C :: 1 : 4 : 2.

1 kg of variety A at Rs.60 is mixed with 4 kgs of variety B at Rs.75 and 2 kgs of variety C at Rs.100.
The total cost for the 7 kgs = 60 + (4 * 75) + (2 * 100) = 60 +300 + 200 = 560.
Cost per kg of the mixture = 560/7 = 80 kgs.

Even assuming that you hit upon the right answer as the last choice, you will still be better of going back from the answer