Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.2)

2. 

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

[A]. Rs. 169.50
[B]. Rs. 170
[C]. Rs. 175.50
[D]. Rs. 180

Answer: Option C

Explanation:

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs. 126 + 135 = Rs. 130.50
2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind
Rs. 130.50 Mean Price
Rs. 153
Rs. x
(x - 153) 22.50

x - 153 = 1
22.50

x - 153 = 22.50

x = 175.50


Suren said: (Jul 29, 2010)  
Totally there are 4kg mixture which costs 153.
therfore,(126+135+x)/4=153
x=351.
Here x is the price for 2Kg.
therefore x=175.50

Ragul said: (Oct 12, 2010)  
Problem is simple.

(126+135+x) * (k+k+2K) =153* (k+K+2K).

When you solve above one, you will get x.

Uma Upadhyay said: (Oct 15, 2010)  
Say the unknown quantity is X.

Then (126*1+135*1+2*x)/(1+1+2)= 153

on solving X= 175.50

Satish said: (Nov 22, 2010)  
x - 153 = 1
------
22.50
will u explaim dis step,,,,,,,Plz,,,,

Ramakhanna said: (May 15, 2011)  
Let the three varieties be A,B,C.
the ratio is given as 1:1:2.
Let x be the price of third variety per kg.
A B C
the cost is: Rs.126/kg Rs.135/kg Rs.x/kg
the amount
(from ratio): (1/4)kg (1/4)kg (1/2)kg
(in kg.)
cost of three varieties per kg = cost of the mixture per kg
so,
(126*(1/4))+(135*(1/4))+(x*(1/2))=153
after making calculation, x=175.5
so, the price of third variety per kg will be Rs.175.5

Shweta Jain said: (Jun 7, 2011)  
Good explanation Ramakhanna.

Ashwini Sriram said: (Jul 14, 2011)  
I agree with Suren. The problem is simpler than it is explained here.

It is just (126+135+2x)/4= 153.

Where x is the price per kg.

Chacha said: (Jul 28, 2011)  
Suren you rocked.

Ankan said: (Sep 2, 2011)  
@Uma Upadhyay.

You are right and you maked its so easy. Thanks and also.

@Suren because you both are following similar process and right one.

San said: (Sep 19, 2011)  
Price of all mixture 126+135+(2*X)
Number of kgs 1+1+2

Therefore mixture price per kg=(price of all mix)/(number of kgs)=153/kg
Hence X=175.5/kg .

Preethi said: (Sep 21, 2011)  
@suren.

In the question 1kg of the mixture is mentioned as Rs 153 na? how can you say 4kg costs 153.

Please explain.

Charan said: (Nov 4, 2011)  
(126+135+2x)/4 = 153
x=175.5rs

Pratima said: (Jan 17, 2012)  
I'm impressed with Uma Upadhyay. Explained with simple method.

Nikhil said: (Feb 14, 2012)  
How come 175.5?

Neelesh said: (May 5, 2012)  
Thanks suren and uma both method much simple as explained here.

Prince Sethi said: (May 21, 2012)  
Simple answer here:
Suppose there are three types of tea:type 1=126kg
Type2=135kg
Type3=xkg
Now
1/4*126=31.5
Again
1/4*135=33.75
Now
2/4*x=x/2

Now addition

31.5+33.75+1/2x=153

x/2=153-65.25

x=175.50

Let me know in-case of any issues

Lokesh Reddy said: (Jun 23, 2012)  
126kg-1st 135kg-2nd xkg-3rd

1 : 1 : 2

(126*1 + 135*1 + 2*x )/ 4 = (153) total mixture.

By solving,

x=170.50.

Pratima said: (Oct 31, 2012)  
How this mean price is calculated in allegation problems?Is there any particular way of calculating mean value?

Sanjeev Sharma said: (Jul 20, 2013)  
OK lets assume that we have 4 kg of mixed sugar so according to ratio provided we will have,

1 kg of 126/kg.
1 kg of 135/kg.
2 kg of x/kg.

We have sold.
4kgs of @153/kg so total = 4*153 = 612Rs.

126+135+2X = 612.
2X = 612-261.
2X = 351.
X = 175.50.

Maya said: (Dec 20, 2013)  
Three mixtures are in the ratio 1:1:2 and prices given that 126, 135, P.

1*126+1*135+2*P = (1+1+2)153.

On solving, we get P = 175.5.

Amit said: (Jan 21, 2014)  
We have ratio of 1:1:2.

So we will assume third as x and eq become,
126+135+2x=4*(153)//per kg that's why * 4 ie (1+1+2) as ratio says,

2x = 612-261.

x = 351/2.

x = 175.50.

Yaw said: (Jan 28, 2015)  
Why do you keep dividing it by 4?

Prakash said: (May 28, 2015)  
126*1/4+135*1/4+x*2/4 = 153.

126+135+2x = 153*4.
261+2x = 612.

x = 175.5.

Hence you have to take per kg how much from total ratio that's what here 126*1/4.

Tanmay said: (Jul 27, 2015)  
@Ramakhanna.

Will you please explain your third step?

Karthika said: (Aug 11, 2015)  
1/4 means?

Md Salman said: (Aug 17, 2015)  
The mixture contain the tea in the ratio of 1:1:2.

So if the mixture contain 1, 1 kg of type 1 and 2 the the weight of third type is 2 kg.

Now 126+135+2*x = 4*153.

261+2*x = 612.
2*x = 612-261.

2*x = 351.
x = 175.50.

Malli Reddy said: (Aug 29, 2015)  
Given the mixture contain in the ratio 1:1:2.

Then the quantities mixed are type1-x;type2-x;type3-2x.

Assume the price of third quantity is y.

Given average cost 153:

From weighted average formula (126x+135x+y2x)/4x = 153.

By solving y = 175.50.

Anil Kishore said: (Nov 17, 2015)  
Why in the explanation?

(x-153)/22.50 = 1.

Sameer Khan said: (Mar 5, 2016)  
Guys it explained in a general way.

Udit said: (Jun 9, 2016)  
It also solve by;

153 - 130.5 = 22.5.

Piyush said: (Jun 28, 2016)  
What if the ratio was something different? how to solve through the same method.

Adhitya said: (Jul 14, 2016)  
(126 + 135 + 2x)/4 = 153,
2x = 35,
x = 170.5.

Parithi said: (Jul 20, 2016)  
Can you explain clearly?

Sucharitha said: (Aug 18, 2016)  
Can you please explain, if suppose the costs of three varieties are given but ratios are not given.
Then what will be the solution?

Bikram said: (Sep 27, 2016)  
Take the average of 126 & 135 = 130.50,
Now deduct 130.50 from 153.
=> 153 - 130.50 = 22.50,
Then add 22.50 with 153.
=> 153 + 22.50,
Finally, the answer is 175.50

Tejas said: (Oct 7, 2016)  
1 : 1 : 2 = 126 + 135 + 2x.
126 + 135 + 2x = 153 * 4.
x = 175.50.

Dinesh said: (Nov 17, 2016)  
Short and simple explanation. Thanks @Suren.

Jitender said: (Dec 6, 2016)  
Simple: (1st quantity * its ratio + second quantity * it's ratio + third quantity * it's ratio)/sum of all ratios = Mean price.

(126x1 + 135x1 + 2xY)/4 = 153,
2Y = 351 , Y = 175.5.

Anu said: (Jan 2, 2017)  
Please explain how to come 22.50?

Manisha Panda said: (Mar 1, 2017)  
@Ashwini.

Your answer was short, precise and understandable. Thanks

Nasir said: (Mar 17, 2017)  
Let there is total x kg of tea and the price of third variety be Rs y per kg.

=> (126*1/4*x) + (135*1/4*x) + (y*1/2*x) = x * 153.
On solving the above eqn, we get y = 175.5.

Manish said: (Apr 2, 2017)  
126 * 1 + 135 * 1 + x * 2 = 4 * 153,
x = 175.5.

Rajat Gupta said: (Apr 16, 2017)  
153-126 = 27,
153-135 = 18,
27+18/2 = 22.5,
153+22.5 = 175.5 easily.

Nidhi said: (Jun 15, 2017)  
How 135? from where did it came.

Mounika said: (Jul 21, 2017)  
1 : 1 : 2 ratio.

So, we can take it as 1/4kg 1/4kg and 1/2 kg.
So, the answer ( 1/4)*126+(1/4)*135+(1/2)*x = 153.

Ayesha Sultana said: (Aug 2, 2017)  
Problem is simple

(126*1 + 135*1 + 2x)/(1+1+2) = 153,
126+135+2x / 4 = 153,
261+2x= 153*4,
261+2x=612,
2x=612-261,
2x=351,
X =351/2,
X=175.5.

Goutam_De said: (Nov 19, 2017)  
(126 + 135 + 2x)/4 = 153,
2x = 612-261=351,
x=351/2,
x = 170.5.

Suresh Arora said: (Dec 29, 2017)  
I cannot understand. Anyone help me to get it.

Priya said: (Jun 1, 2018)  
By the diagram, we can choose right side after subtraction first. So it will be x-153 and then choose left after subtraction 22.5. Divide the values x-153/22. 5 we can get the answer.

Tushar Agarwal said: (Jul 19, 2018)  
126x + 135y + Xz/x + y+z = 153;

consider this formula for ratios and we know x:y:z=1:1:2.
So substituting x, y and z and calculating X we get X=175.50.

Saidul said: (Aug 2, 2018)  
X:Y:Z=1:1:2 (total=4).
153tk/kg (total amount=153*4=612tk),
1st two(135+126=261tk),
3rd=612-261=351tk,

As 3rd variety was 2kg, then 1kh price is=315 ÷ 2=175.50tk (Ans.)

Naveen Gaddam said: (Aug 23, 2018)  
Give the ratio of three type of sugars are in =1:1:2.

1/4 kgs of the first two types and 2/4 kgs of third type sugar.

assume third type sugar price=x per kg.
(1/4)*126+(1/4)*135+ (2/4)*x=153.
(126+135+2x)/4 = 153.
261+2x=612..
2x=351.
x=175.50.

Sathish said: (Dec 6, 2018)  
1 : 1 : 2.

So 126+135/2=130.5 third varity.
(1*126)+(1*126)+(2*130.5) = 612 total price.
612 - 126 - 135 = 351 third varity price.
351/2 = 175.5.

Naveen said: (Jan 24, 2019)  
Simple formule:

(1:1:2)/4=153
(126+135+2X)/4 = 153,
261+2X = 4 * 153
261+2X = 612,
2X = 612-261,
2X = 351,
x = 175.5.

Gopeswar said: (Mar 13, 2019)  
The basic mixture and alligation formulae say:

Average =(N1A1+N2A2+....+NnAn)/(N1+N2+.....Nn)
Therefore: 153=(126*1+135*1+2*x)/(1+1+2).
solve and find x, here x is the price of the third variety of price.

Boopathy said: (Jul 2, 2019)  
I am not understanding. Please explain to me.

Rachana said: (Jul 13, 2019)  
@Boopathy.

As the ratio given is 1:1:2.
So, we apply alligation for this. By observing this 1 is repeated twice so take average of it . And you get the value of c=130.5 Rs and value of d=153Rs is given in alligations rule.

Rashmitha said: (Oct 1, 2019)  
Have anyone got 164.25 as answer.

Rakesh said: (Aug 30, 2020)  
Total units(1:1:2)= 1+1+2=4 (4kgs).
Total sum =avg * no. of units =153 * 4 = 612.
Remove first two =612-126-135 = 351.
Hence as the third variety holds 2 units (i.e. 2kgs).
1kg price = 351/2 =175.5.

In short:
Price of third variety = (153* 4 - 126 - 135)/2 =175.5.

Niharika said: (Nov 15, 2020)  
Third Verity = x
126 * 1 + 135 * 1 + X * 2/1 + 1 + 2 = 153.
X = 175.50.

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