The ratio, in which tea costing $192 per kg is to be mixed with tea co

Question

The ratio, in which tea costing $192 per kg is to be mixed with tea costing $150 per kg so that the mixed tea when sold for $194.40 per kg, gives a profit of 20%.

A. 2:5
B. 3:7
C. 1:2
D. 3:5
E. 4:5

Bunuel · Accepted Answer

To achieve a profit of 20% when selling the mixed tea at $194.40 per kg, the cost of the mixture must be $194.40/1.2 = $162 per kg.

Let's assume that a fraction x of the $192 tea blend should be used, and thus, the remaining fraction (1 - x) would be from the $150 tea blend. Setting up the equation  192x + 150(1 - x) = 162 , we find  x = \frac{2}{7}  and  1 - x = \frac{5}{7} . Therefore, the ratio between the two blends is 2:5.

Answer: A.

Deepakjhamb · Answer

194.4 = Cp * ( 1 +20 / 100 )

Cp = 162

By allegation method

Ratio = ( (162-50 ) / ( 192 - 162 ) = 2 : 5

So ans is a

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Abhishek009 · Answer

150 _______________________ 192
 ____________ 162 ____________  As, \frac{194}{120}*100 = 162 
30 _______________________ 12

Or,  10 : 4 = 5 : 2 , Thus Answer must be (A)

CEdward · Answer

Great question. So I finally understood how to approach something like this. It's nothing more than a weighted average question, with a minor twist.

The first thing to understand is that after you've mixed both things, you would end up with a selling price that lies somewhere between 150 and 192. These are the so-called boundaries of the weighted average. However, here, the stem states that the price at which a 20% profit is made is 194.40, which makes sense considering it's  higher  than the upper boundary of the weighted average. So to get that weighted average what we want to do is divide 194.40 / 1.2

194.40/1.2 is 162.

OK now what?

The next thing is figuring out the ratio of the units that need to be sold to get 162. To do that use the WA formula:

Let A be the first tea and B be the second.

150A + 192B / A + B

Plug in each of the answer choices to see which one gives 162.

Answer is A.

Lodz697 · Answer

Hello  Bunuel , could you provide an explanation for the question?

Thanks in advance!

Yeetyeti38 · Answer

I also find it helpful when doing it this way to assess which answer choices will be realistic options

Once you arrive at knowing the weighted average will be 162, you can estimate how much of each element will be needed. 162 is 12 away from 150 but 30 away from 192, so we can infer that the amount of the 150 element will be notably greater than the 192 element.

That way you can start by testing only A or B since C, D and E are all fairly close together.

Lodz697 · Answer

How's this method called?

bumpbot · Answer

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The ratio, in which tea costing $192 per kg is to be mixed with tea co

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