Alligations or Mixtures

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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 : 2 : 4


3 : 7 : 6


1 : 4 : 2


None of these

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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:

Step 2: 
Find out the ratio of $Q_b:Q_c$ using alligation rule:

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:
$=60+(4 \times 75)+(2 \times100)$

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)

Shubham Yadav

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 ??


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

Please explain.


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

If want to know more about this, why don't you check up some theory first?


I found the theory mentioned on this website as well. Just visit the introduction section:

Rahul Kumar

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


And why do you say that?