Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.4)

4. 

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

[A]. 4 litres, 8 litres
[B]. 6 litres, 6 litres
[C]. 5 litres, 7 litres
[D]. 7 litres, 5 litres

Answer: Option B

Explanation:

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3
4 4

Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 1
2 2

Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5
8 8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can    C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8

Ratio of two mixtures = 1 : 1 = 1 : 1.
8 8

So, quantity of mixture taken from each can = 1 x 12 = 6 litres.
2


Moncy said: (Oct 29, 2010)  
If it is 6litres of milk and 6litres of water making 12litres of the mix,then does not it mean that milk and water is 50% and 50%??how will it be in the ratio 3:5 to satisfy the requirement??Please explain this..

Mahendra said: (Nov 13, 2010)  
@moncy The solution to this problem is right

Ans is [B] 6 litres, 6 litre

6 liters from first can gives 1.5 litre of water and 4.5 of milk
6 liters from second can gives 3 litres of water and 3 litres of milk
so, (1.5+3)/(4.5+3)= 4.5/7.5 = 0.6 = 3/5

Manish said: (Dec 17, 2010)  
Initially water and milk percent was 25% water and 75%milk
in 2nd container 50-50%

finally milk was 12 litre
ratio was 3:5 means 3x water and 5x milk s0 5x=12 ;x= 12/5
water 36/5
milk percentage 12/(12+36/5)=62.5
soincrease in milk percentage 12.5%each so omly one option is matching

Nagendramurthy said: (Jun 23, 2011)  
Friends see can also solve the problem..
initially water and milk in first can are in 1/4 and 3/4
in the second can 1/2 and 1/2

therefore total (1/4)+(1/2) of water and (3/4)+(1/2)

i.e (3/4) of water and (5/4) of milk

If we compare it already in the ratio of 3:5

So we have add equal amount of water and milk in order to maintain the ratio same..

Charan said: (Nov 4, 2011)  
Lets take total in terms of mixture in x & y
new water mixture = x/4+x/2
milk = 3y/4 + y/2
ratio comes out as x:y = 3:5
thats its self gives the new mixture
2x=12 or 2y=12
6ltr n 6ltr

Kunal said: (Jun 19, 2012)  
CAN 1 -water 1/4, milk 3/4 x.

CAN 2 - water 1/2, milk 1/2 y.

Required " 3/8, " 5/8.

x/4+y/2=3/8 3x/4+y/2=5/8.

Solving x=1/2, y=1/2.

x:y = 1:1.

So 6, 6.

Vikas said: (Aug 8, 2012)  
Let x and y liters from the can to be mixed to make 12 liters of milk.

Can1 has x/4 (water) and 3x/4 (milk).

Can2 has y/2 (water) and y/2 (milk).

So new ratio of water to milk is.

(x/3+y/2) / (3x/4+y/2) =3/5.

And x+y=12.

X=6 and y=6.

Ajinx999 said: (Aug 31, 2012)  
Let x L of milk be removed from can A (25% water). Since, 12 L of milk is finally required, (12-x) L of milk is removed from can B (50% water).
Considering following ratio

(water from A) + (water from B) 3
--------------------------------------- = ---
(pure_milk from A) + (pure_milk from B) 5

(1/4)x + (1/2)(12-x) 3
-------------------- = ---
(3/4)x + (1/2)(12-x) 5

Solving for x, x = 6
So 6 L is removed from can A and (12-6) = 6 L is removed from can B.

Amisha said: (Sep 1, 2012)  
Can1 75% milk Can2 50% milk

mean 62.5%(3:5,so milk = 5/8*100 = 62.5)
12.5 12.5

so, ratio is = 1:1 so, in 12 lit mixture 6lit from 1can and 6 lit from 2 can

Anil Kumar Jat said: (Dec 18, 2012)  
With the help of option

M W
6 3 : 1
6 1 : 1
M=3+4.5=7.5
W=3+1.5=4.5

THERFORE W:M=4.5:7.5=3:5 IS GIVEN SO ANSWER 6,6 IS CORRECT.

Kailash Chandra said: (Jan 31, 2013)  
Let,
25+50=75 (water).
75+50=125(milk).

75/125=3/5.
3/5=3/5.

Obviously mix ratio 1:1.
So, 12 lit=6 and 6.

Vikram Ojha said: (May 24, 2013)  
1st can Water:milk = 1:3.
In 2nd can water:milk = 1:1.

In 12 liters = water:milk = 3:5.

So in 12 liters we have 3(12)/8 = 4.5 liter of water.

Lets us consider we have x liters of water in new mix.

So our equation will be,
1(x)/4 + 1(x)/2 = 4.5.
x = 6 liters.

So amount of water in new mixture = 6 liters.
And that of milk will be = 12-x = 6 liters.

Vivek Kumar said: (Aug 7, 2013)  
If we take mixture of both the can be x.

Than (x/4+x/2)/(3x/4 + x/2) = 3x/5x = 3/5.

The ratio comes 3/5 only if we have equal amount of milk(x here). So, according to question,

x+x=12;

2x=12.

x = 6.

12-6 = 6.

So, Answer is 6, 6.

Meeran said: (Dec 24, 2013)  
Water : Milk
Can 1 1 : 3
Can 2 1 : 1

Required ratio = 3 : 4.

Therefore ratio of can1+ can2+ added quantity = required quantity.

1+1+1 : 3+1+1 is the only possible way, ratio added must b,
1 : 1.

Hence, option B, 6 : 6 is only possible which can give 1 : 1 ratio.

Anand Patel said: (Jun 21, 2014)  
From the first can mixture is X liter.

From the first can mixture is Y liter.

NOW X + Y = 12.

IN 12 LITER portion of water is 4.5 and milk IS 7.5 LITER.

X( (1/4)+ (1/2))+ Y ((3/4)+(1/2))= 4.5 + 7.5.

SO X( (1/4)+ (1/2))= 4.5 => X= 6 LITER.

Y ((3/4)+(1/2)) = 7.5 +> Y = 6 LITER.

Vaishnavi said: (Jul 12, 2014)  
Please explain me in a simple way guys?

I can't get the logic?

Ajay said: (Jul 21, 2014)  
Cont 1 has 25% water and 75% milk.
Cont 2 has 50% water and 50% milk.

We take x lit mixture from cont 1.
25x/100 lit water and 75x/100 lit milk.

And take y lit mixture from cont 2.
50y/100 lit water and 50y/100 lit milk.

Ratio of water to milk = 25x+50y/75x+50y = 3/5.

From here x = y.
And total milk = 12 lit.

25x/100+75x/100+50y/100+50y/100 = 12 lit.

Put x = y.

Get answer as x = 6 and y = 6 lit.

And enjoy your day!

Gokulpriya said: (Sep 7, 2014)  
How did 5/8 become mean prize what is this value?

Sri Divya said: (Nov 5, 2014)  
Hi friends, Please explain how 5/8 became the mean price?

How to calculate mean price?

Sri said: (Feb 28, 2015)  
Can anybody tell me how 5/8 arrived here?

Dhanwin said: (May 8, 2015)  
Different approach:
==============

Can 1 ---- 25% water + 75% milk.
Ratio ---- 1:3 (25/75 = 1/3).

Can 2 ---- 50% water + 50% milk.
Ratio ----- 1:1 (50/50 = 1/1).

If I take p liters from can 1 and q liters from can 2.

So that total should be 12 liters with water : milk = 3 : 5.

So I get following equation.

P+q/3p+q = 3/5 -------- (equation 1).

Now try checking the given options in questions and the answer should be the "option" which satisfies the (equation 1).

Ex:

Let p = 6 and q = 6.

Then 6+6/(3*6+6) = 3/5.

So the equation 1 is satisfied. So the answer is 6 liters from can 1 and 6 liters from can 2.

Other options given won't satisfy the (equation 1).

Dhruv Sahni said: (Jun 6, 2015)  
Container A has 25% water, Container B has 50% of water and after mixing these two final mixture has 3/8 -> 37.5% of water.

So by allegation method the ratio of A and B in final mixture will be 25% 50% 37.5%.

50%-37.5% : 37.5%-25%.

= 12.5% = 12.5% = 1:1.

So Ratio of A:B in final mixture is 1:1, hence in 12 liter of mixture there will be 6L of A and 6L of B.

Anu said: (Aug 13, 2015)  
Please somebody clarify the logic behind that question in short way.

Megh said: (Sep 11, 2015)  
Can any one tell me how did you get 5/8?

Shashi Bhushan said: (Sep 25, 2015)  
Let x and y liters from the can to be mixed to make 12 liters of milk.

Can 1 has x/4 (water) and 3x/4 (milk).

Can 2 has y/2 (water) and y/2 (milk).

So new ratio of water to milk is.

(x/3+y/2)/(3x/4+y/2) = 3/5.....(1).

By the question.

x+y = 12.....(2).

To solve these equation.

x = 6, y = 6.

Parvy Govil said: (Nov 6, 2015)  
Let x litres of A and y litres of B is extracted x+y = 12.

Milk quantity = 1/5x+1/2y = 3/5(4/5x+1/2 y).

x = 5 litres.
y = 7 litres.

Ramakrishna said: (Dec 2, 2015)  
In 1st 25% water, 2nd 50% water.

Then resultant ratio given that 3:5, if 3+5 is 100% then 3 is 37.5% water.

That is subtracted from 37.5-25 = 50-37.5 = 12.5.

Then those two values are same so ratio is 1:1 answer 6 lit, 6 lit.

If you do for milk also get same answer.

Soumya said: (Dec 2, 2015)  
If a chemical solution contains 30% water & 70% Alkali. What quantity of water should be added to 6 liter of solution. So that water content become 40%.

Stalin said: (Feb 4, 2016)  
Can any explain how did we get 5/8?

Bakhtiar said: (Feb 7, 2016)  
Can anyone help me to understand this problem?

Adithi said: (Feb 27, 2016)  
In the first can water and milk ratio is 1 : 3 and in the second it is 1 : 1.

Mixture is 3 : 5 now sub 1/4 and 3/8 (water) it is 1/8. Next 1/2-3/8 it is 1/8 (milk). So the water and milk ratio is 1 : 1. Hence in total of 12 litres 6 litres milk and 6 litres water.

Dhananjay said: (Mar 7, 2016)  
Can somebody help me do the same sum with ratios 2:1, 1:3 and final needed ratio 1:1 the ratios being milk:water in the mixture.

Pranjal Patel said: (Jul 2, 2016)  
It's really easy but I can do it in an easier way by another method.

Naveen said: (Jul 6, 2016)  
I'm confusing, please clearly explain the solution.

Cipher Gopal said: (Aug 25, 2016)  
@Amisha, can you explain how we get 5/8?

Anil said: (Aug 28, 2016)  
See, first of all understand that the resultant mixture contain water and milk in ratio 3 : 5.

So, water concentration is 3/8 = P (resultant one).
Now we have first mixture (can) water concentration 1/4 = P1.
Similarly second mixture (can) water concentration 1/2 = P2.
Q1/Q2 = (P2 - P)/(P - P1).
Will give the answer as 1 : 1.

So, the answer is B.

Sabarinath S said: (Aug 29, 2016)  
Easy method: Take from options

1. Eliminate all answer whose sum is not 12L (here all r 12).
2. 3x/5x new ratio , take option A gives 3 * 4/5 * 8 not equal to 3 : 5.
So, b) 3 * 6/5 * 6 is 3 : 5.

Yuhi said: (Sep 20, 2016)  
The ratio given is 3 : 5 water to milk means 5 parts of milk and 3 parts of water in total 8 parts (3 + 5). So mean here is 5/8 because we need to find out the milk percent.

Dinesh said: (Oct 4, 2016)  
I think the questions is wrong because 12 is not only milk mixture, 12 is a total mixed mixture.

Saurabh said: (Oct 11, 2016)  
Can anyone explain me how "Milk in 1 litre mix in 1st can =3/4 litre come?

Nitin Garg said: (Oct 13, 2016)  
Let one can contain 100 litres of liquid (water + milk).
Now, in the first can, there is 25 l of water and 75 l of milk.
In the second can, there is 50 l of water and 50 l of milk.
Now let he takes y l of liquid from can 1 & y l of liquid from can 2.
Now the quantity of water in this y l of liquid will be ((25/100) y + (50/100) y) = (3/4) y.
But the quantity of water in 12 l of milk is ((3/8) * 12).
Equate (3/4) * y = (3/8) * 12.
y = 6.
So he will take 6 l of liquid from both the cans.

Skk said: (Oct 27, 2016)  
Water = X.
Milk = Y.

Can1 contains Water = X/4 and milk is = 3Y/4.
Can2 contains Water = X/2 and Milk is = Y/2.

Total water and milk ratio = 3/5.

But water and milk = X + Y = 12.

Water/milk Ratio = X/4 + X/2/3Y/4 + Y/2= 3/5.
Substitute X = 12 - y.
We will get X = 6 & Y = 6.

Pradeep said: (Dec 31, 2016)  
Thanks a lot @Kailash Chandra.

Shambhu said: (Jan 18, 2017)  
Let x l & y l taken from can A(1:3) & can B(1:1) resp.
In new 12 of mixture (ratio 3:5).
x + y =12.
Water= 3*12/8 & milk= 5 * 12/8.

Then now, x/4 + y/2 = 3*12/8. (W)
And, 3x/4 + y/2 = 5*12/8. (M)

Solving both equations, we get;

x =6l & y = 6l.

Odett said: (May 18, 2017)  
Very good explanation @Moncy.

Kabir said: (Nov 17, 2017)  
12 liter milk or mix. I am confused. Is this question in right mood. Please anyone explain the question.

Sridharsan said: (Dec 9, 2017)  
Actually, we need 12 ltrs of milk, here where is 12 ltr of milk, 6+6=12 (it is a mix, not purely milk).


Please explain in detail.

Sravani said: (Mar 28, 2018)  
So in this problem,

5/8 is taken as the total mixture is in the ratio 3:5(water:milk).
so as we are calculating for milk quantity in the aligation process, the milk quantity is according to ratio 5/3+5=5/8.

Hope you understand this.

Nani said: (Jan 14, 2019)  
Nice explanation, thanks a lot @Vivek Kumar.

Guru Prasad said: (Feb 26, 2019)  
Alternate method:
-
CAN:1---> 25% water and the remaining 75% milk.
CAN:2---> 50% water and 50% milk.

Given ratio is 3:5. since only the quantity of milk is to be estimated therefore there is 5/8 of milk present in the mixture. converting this into percentage it is 62.50%.

By using allegation:-
{75% = M & 50% = N and D = 62.50%}--------> General Assumption.

M - D = 75% - 62.50%
= 12.50%.

D - N = 62.50% - 50%,
= 12.50%.

(M - D) : (D - N) = 1 : 1.

Therefore the quantity of milk to be mixed from each of the containers in order to 12 litres of milk is;

(1/2) * 12
= 6 litres. since the obtained ratio is 1:1 therefore from container-1 it is 6 litres and from container-2 it is also 6 litres.

Amit Ambadkar said: (Mar 4, 2019)  
Let's see 2 methods to solve the problem.
Let 1st can contain x lit of mixture(means 0.25x lit water and 0.75x lit milk).
2nd can contain y lit of mixture(means 0.5y lit milk and 0.5y lit water).
After mixing both the ratio of water to milk is 3:5.
So,
(0.25x+0.5y):(0.75x+0.5y) = 3:5.
After solving x:y=1:1,
And we have x+y=12,
So x=y=6.

Amin said: (May 17, 2019)  
Why we take 12 litres of milk as x+y=12?

Prakhar said: (Jul 27, 2019)  
Best explanation, thanks @Ajay.

Dinesh said: (Jul 31, 2019)  
How will you find the quantity of mixture?

Sabbir said: (Feb 16, 2020)  
You can solve the math in this way as well,

In can1 there is 25% (1/4) water and 75% (3/4) milk.
Again, in can2 there is 50% (1/2) water and 50% (1/2) milk.
So, total volume of water = 1/4+1/2 = 3/4.

Total volume of milk = 3/4+1/2 = 5/4.

Now, as per the question, the ratio of water and milk must be 3x and 5x.

So, we can write, 3/4:5/4 = 3x:5x.
Or, 3/4* 5x = 5/4 * 3x.
Or, 15x/4 = 15x/4.

That's to say the volume of water and milk must be the same. Hence the answer will be 6 liters.

Andy said: (Apr 1, 2020)  
Three parts milk and 1 part water in one container and 1 part milk and 1 part water in the second container.

Representing the milk 3x/4+1x/2 = 7.5(5/8*12) Solving x you get 6.
Representing the water 1x/4+1x/2 = 4.5(3/8*12) Solving x you get 6.

Surya said: (Jun 3, 2020)  
Can anyone tell how we are multiplying 1/2 with 12?

Harshada said: (Jun 10, 2020)  
Well explained @Kunal.

Muslih said: (Jun 10, 2020)  
As per allegation, we obtained that same quantity are taken from each Can.

So (.75)*x+(.5)*x=12 milk in the new mix, where x-> quantity mixer taken from can1 and can2(1:1).
X=12*4/5.

MILK FROM CAN 1 is = (.75) * 12 * 4/5 = 36/5 = 7.2..
Milk from can 2 is =.(.5) * 12 * 4/5 = 24/5 = 4.8.

Hence answer for the quantity of milk collected from each CAN to get the 12lit of milk is 7.2 and 4.8 respectively.

Am I right?

Sasi said: (Dec 18, 2020)  
x -> quantity from A.
y -> quantity grom B.
x + y = 12;
0.25x + 0.5y = (3/8)*12.
Solving for x and y we get an answer.

B.M. Nasim Reza Anik said: (Feb 13, 2021)  
If 1 litre is drawn from the 1st container, we get 0. 25L water and 0. 75L milk and if 1 litre is drawn from the 2nd container, we get 0.5L water and 0.5L milk.

By combining 1L from each of the two containers, we get 0. 75L water and 1.25L milk. In which water to milk is in the ratio of 3:5.

Thus we need 2+2+2+2+2+2 to get 12L in total and 6L from each of the containers.

Hardik said: (May 1, 2021)  
The initial ratio of water to milk in can 1 is 1:3.
Initial ratio of water to milk in can 2 is 1:1.
If we add both then we get the ratio of water to milk 2:4.
It is said that this ratio becomes 3:5.
So from 2:4, it becomes 3:5.

As we can see there is an equal amount of change 3-2 = 1 and 5-4 = 1.
Therefore the quantity also should be in the ratio of 1:1.
Hence the answer is 6:6.

Shivam said: (Jun 1, 2021)  
@Hardik.

Nice explanation!

Xiyo said: (Jun 7, 2021)  
Nice Explaination @Hardick!

Cosmi said: (Jul 3, 2021)  
Ans :
For Each liter of the mixture in A we can see 0.25l of Water and 0.75l of Milk.
For Each liter of the mixture in B There will be 0.5l of Water and 0.5l of Milk.


Let x liter of mixture taken from A and y liter of mixture taken from B.
WKT the final ratio should be 3:5 and We need to find how much liters should be taken from both A and B.
Water/Milk = 0.25x + 0.75y/0.75x + 0.5y =3/5,
===>after simplification x = y ..take equal amount of liters in A and B that makes 12l.

Shrti said: (Jul 10, 2021)  
I can't understand please explain in simplest way.

Kirthi said: (Aug 1, 2021)  
How it comes 3/4 in that? Please explain me.

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