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

Question

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

Gnpth · Accepted Answer

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

Please see the below links for theory. 1. Work Problem Made Easy 2. Mixture Problems Made Easy 3. Word Problem Made Easy

bazc · Answer

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

Temurkhon · Answer

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

mvictor · Answer

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.

gracie · Answer

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

KarishmaB · Answer

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)

GMATGuruNY · Answer

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.

A

Mo2men · Answer

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

GMATGuruNY · Answer

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.

To apply alligation here would likely be more confusing than helpful.

bumpbot · Answer

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