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Mixtures and Alligations - Quant/Math - CAT 2009
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 |
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(2) |
3 : 7 : 6 |
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(3) |
1 : 4 : 2 |
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(4) |
None of these | Correct Answer - (3)
Solution:
The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96 => Cost =  = 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 QA : QC using alligation rule 
Step 2. Find out the ratio of QB : QC using alligation rule 
Step 3. QC, the resultant ratio of variety c can be found by adding the value of QC 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 QA : QB : QC :: 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.
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