# 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

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.