# Difficult Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. 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%?
 ✖ A. 1 : 2 : 4 ✖ B. 3 : 7 : 6 ✔ C. 1 : 4 : 2 ✖ D. None of these

Solution:
Option(C) is correct

The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96 ⇒ Cost $=\dfrac{96}{1.2} =$ Rs.80 / kg.

Let the three varieties 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:
$\dfrac{Q_a}{Q_c}=\dfrac{100-80}{80-60}=\dfrac{1}{1}$

Step 2:
Find out the ratio of $Q_b:Q_c$ using alligation rule:
$\dfrac{Q_b}{Q_c}=\dfrac{100-80}{80-75}=\dfrac{4}{1}$

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 maybe 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 7kgs:
$=60+(4 \times 75)+(2 \times100)$
$=60+300+200=560$

Cost per kg. of the mixture $= \dfrac{560}{7} = 80$ 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

Edit: Many users ( Vichal RastogiShubham Yadav) have arrived at the final ratio as $Q_a : Q_b : Q_c :: 4 : 4 : 5$, which is also the CORRECT answer. BE WARNED that such problems have multiple correct answers, so you are better served by checking the options first.

## (8) Comment(s)

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Vichal Rastogi
()

if no options are given can one of the answer be 4:4:5 ... ??

Vichal Rastogi
()

Cant the answer be 4:4:5 ??

Vijaya
()

I do not understand - why are we adding in step 3?

Riya
()

In order to arrive at the correct ratio, we add the COMMON ingredient (in this case its $Q_c$).

Riya
()

I found the theory mentioned on this website as well. Just visit the introduction section: http://www.lofoya.com/Aptitude-Questions-and-Answers/Alligation-or-Mixture/intro#Mixture-Containing-3-Ingredients

Rahul Kumar
()

the answer is wrong. It should be $Q_a:Q_b:Q_c = 1:4:1$

Matt
()

And why do you say that?