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Robin mixes two liquids, one blue in colour and other red in

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Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 27 Aug 2014, 00:24
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14
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B
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Robin mixes two liquids, one blue in colour and other red in colour in the ratio 3:1 and sells the mixture at the rate of $15 per litre, thereby making a 20% profit on his outlay. The blue liquid costs Robin $2 per litre lesser than the red liquid. How much does a litre of red liquid cost?


A) $14
B) $13
C) $12
D) $11
E) $10


Source: 4Gmat

Hi can someone share strategies and concepts on Ratios, Mixtures and Propotion :(
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Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 27 Aug 2014, 01:51
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In mixture problem always try to make an equation,

Questions says Robin sells the 1 litre of mixture for $15.

The ratio given is 3:1 for Blue: Red.

Let the multiplier for ratio be 1--(take small and simple terms which is easy for calculation or multiple of 10.

So we have 3 litre of blue liquid and 1 litre of red liquid. So total of 4 litre,

Robin sells 4 litre of mixture for=4* 15= $60

We know that Blue cost $2 less than the red per litre.

So B= R-2 per litre.

here we have 3 litre of blue= \(3(R-2)\)

Now since the question says he gets 20% profit. The equation will be,

\([3(R-2)+ R] + \frac{20}{100} [3(R-2)+ R]= 60.\)

On simplifying,

\(1.2[3R-6+R]= 60\)

\(1.2(4R-6)=60\)

\(4R- 6= 50\).

\(4R= 56\)

\(R= 56/4= 14\)

The answer is A. Hope it helps :)


Please see the below links for theory.

1. Work Problem Made Easy
2. Mixture Problems Made Easy
3. Word Problem Made Easy
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Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 28 Aug 2014, 04:26
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Alternative Same approach as above but finding total cost first makes it easier:

Let x be the required cost per litre of red paint.

Take 4 litres of this mixture.

Sold at 60 with a profit of 1/5th of total cost. So, total cost will be 1/6th less than 60; total cost = 50.

3(x-2) + 1(x) = 50

x = 14
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Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 14 Sep 2015, 00:33
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B : R = 3 : 1
Cost of Red = x
Cost of Blue= x-2
What is the x?

Cost of mixture =(100/120)*15 => 12.5 dollars

0.75(x-2)+0.25x=12.5 => x=14

A
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Re: Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 11 Jan 2016, 19:23
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since we have 3/1 B/R, we can assume we have 4 liters in total. thus, 60$/total sold. 60=1.2x, where x is the cost, and 1.2 is the revenue. thus, x=60*10/12 = 50.

now, 3B+R=50.
B=R-2.
substitute:
3(R-2)+R=50
3R-6+R=50
4R=56
R=56/4
R=14.

A.
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Re: Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 25 Nov 2017, 15:25
alphonsa wrote:
Robin mixes two liquids, one blue in colour and other red in colour in the ratio 3:1 and sells the mixture at the rate of $15 per litre, thereby making a 20% profit on his outlay. The blue liquid costs Robin $2 per litre lesser than the red liquid. How much does a litre of red liquid cost?


A) $14
B) $13
C) $12
D) $11
E) $10


cost of liter of red liquid=c
total cost=3(c-2)+c=4c-6
total revenue=4*15=$60
1.2*(4c-6)=60
c=$14
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Re: Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 01 Mar 2019, 05:37
alphonsa wrote:
Robin mixes two liquids, one blue in colour and other red in colour in the ratio 3:1 and sells the mixture at the rate of $15 per litre, thereby making a 20% profit on his outlay. The blue liquid costs Robin $2 per litre lesser than the red liquid. How much does a litre of red liquid cost?


A) $14
B) $13
C) $12
D) $11
E) $10


Source: 4Gmat

Hi can someone share strategies and concepts on Ratios, Mixtures and Propotion :(


Selling price of the mix is $15 and profit is 20%.
Cost Price * (6/5) = 15
Cost Price = 25/2

This is the average cost price of the mix when you put together blue liquid and red liquid.

25/2 = (Cb*3 + Cr*1) / (3 + 1)

3Cb + Cr = 50

Now we know that Cb (cost of blue liquid) is 2 less than Cr (cost of red liquid)
3(Cr - 2) + Cr = 50

Cr = $14

Answer (A)
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Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 01 Mar 2019, 06:17
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alphonsa wrote:
Robin mixes two liquids, one blue in colour and other red in colour in the ratio 3:1 and sells the mixture at the rate of $15 per litre, thereby making a 20% profit on his outlay. The blue liquid costs Robin $2 per litre lesser than the red liquid. How much does a litre of red liquid cost?


A) $14
B) $13
C) $12
D) $11
E) $10


At a rate of $15 per liter, the selling price for a 4-liter mixture composed of 3 liters of blue and 1 liter of red = 4*15 = 60.
20% profit = 120% of the cost = 6/5 of the cost.
Since the selling price is 6/5 of the cost, the cost is 5/6 of the selling price:
Cost of 3 liters of blue and 1 liter of red = 5/6 * 60 = 50

We can PLUG IN THE ANSWERS, which represent the cost for each liter of red.
The prompt indicates that each liter of blue costs $2 less than each liter of red.
When the correct answer is plugged in, 3 liters of blue and 1 liter of red will cost $50.

B: $13, implying that the cost of each blue liter = 13-2 = 11
Cost of 3 liters of blue and 1 liter of red = (3*11) + 13 = 46
Since the cost is too low, a greater answer choice is needed.


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Re: Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 02 Mar 2019, 04:38
GMATGuruNY wrote:
alphonsa wrote:
Robin mixes two liquids, one blue in colour and other red in colour in the ratio 3:1 and sells the mixture at the rate of $15 per litre, thereby making a 20% profit on his outlay. The blue liquid costs Robin $2 per litre lesser than the red liquid. How much does a litre of red liquid cost?


A) $14
B) $13
C) $12
D) $11
E) $10


At a rate of $15 per liter, the selling price for a 4-liter mixture composed of 3 liters of blue and 1 liter of red = 4*15 = 60.
20% profit = 120% of the cost = 6/5 of the cost.
Since the selling price is 6/5 of the cost, the cost is 5/6 of the selling price:
Cost of 3 liters of blue and 1 liter of red = 5/6 * 60 = 50

We can PLUG IN THE ANSWERS, which represent the cost for each liter of red.
The prompt indicates that each liter of blue costs $2 less than each liter of red.
When the correct answer is plugged in, 3 liters of blue and 1 liter of red will cost $50.

B: $13, implying that the cost of each blue liter = 13-2 = 11
Cost of 3 liters of blue and 1 liter of red = (3*11) + 13 = 46
Since the cost is too low, a greater answer choice is needed.



Dear GMATGuruNY

1- Is not the ratio of costs same as ration of amounts of both liquids i.e. 3/1?

2- I know your solution is the better, but Can you use alligation?

Thanks
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Re: Robin mixes two liquids, one blue in colour and other red in  [#permalink]

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New post 03 Mar 2019, 05:31
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Quote:
Dear GMATGuruNY

1- Is not the ratio of costs same as ration of amounts of both liquids i.e. 3/1?


The cost ratio and the volume ratio can be quite different.
While the red liquid constitutes 1/4 of the total volume, it does not necessarily constitute 1/4 of the total cost.
Consider the following case:
Cost of the blue liquid = $1 per liter.
Cost of the red liquid = $1000 per liter.
Cost of 4 liters of a 3:1 solution = (3*1) + 1000 = $1003.
In this case, much more than 1/4 of the total cost -- in fact, almost 100% of the total cost -- is attributable to the red liquid.

Quote:
2- I know your solution is the better, but Can you use alligation?

Thanks


To apply alligation here would likely be more confusing than helpful.
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Re: Robin mixes two liquids, one blue in colour and other red in   [#permalink] 03 Mar 2019, 05:31
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