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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 26 Aug 2014, 23:24
2
10
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:42) correct 39% (03:20) wrong based on 191 sessions

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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, 00:51
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1
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, 03:26
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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 13 Sep 2015, 23:33
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, 18:23
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, 14:25
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
A
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Re: Robin mixes two liquids, one blue in colour and other red in &nbs [#permalink] 25 Nov 2017, 14:25
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