Mixtures Question: Mixing 3 Variants

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

Question

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      Choice (3). 1 : 4 : 2

Explanatory Answer

Step 1: Compute cost of 1 kg of the mixture
The resultant mixture is sold at a profit of 20%. The selling price is Rs.96/kg
i.e., cost + 20% of cost = 1.2 (cost) = Rs.96
=> cost of the mixture = \\frac{96}{1.2}) = Rs.80/kg.

Let the three variants be A, B, and C and let their cost per kg be 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 the 3 variants should be mixed.
Step 2: Find out the ratio of Q_A : Q_C using alligation rule \\frac{{Q}_{A}}{{Q}_{C}}) = \\frac{100-80}{80-60}) = \\frac{1}{1}) = 1 : 1
Step 3: Find out the ratio of Q_B : Q_C using alligation rule \\frac{{Q}_{B}}{{Q}_{C}}) = \\frac{100-80}{80-75}) = \\frac{4}{1}) = 4 : 1
Step 4: Q_C, the resultant ratio of variant 'C' can be found by adding the value of Q_C in step 1 and step 2 = 1 + 1 = 2.
The resultant ratio Q_A : Q_B : Q_C :: 1 : 4 : 2.

Note
However, if you try and solve this problem using the above method, you will end up spending more than 2, and may be 3 minutes on this question, which is not wise way to manage time in the test.
The best way to solve a problem of this kind in CAT or TANCET is to go from the answer choices as shown below.

Let us go with the correct answer. They are mixed in the ratio 1 : 4 : 2.
1 kg of variant A at Rs.60 is mixed with 4 kg of variant B at Rs.75 and 2 kg of variant C at Rs.100.
The total cost for 7 kg of the mixture = 60 + (4 * 75) + (2 * 100) = 60 +300 + 200 = Rs.560.
Cost per kg of the mixture = \\frac{560}{7}) = Rs.80 which matches the cost we arrrived at in the Step 1.
Even assuming that you hit upon the right answer as the last choice, you will still be better of by back substituting choices for this question.

  The correct answer is Choice (3).