Aptitude - Alligation or Mixture - Discussion

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

Let those 3 items be a,b,c.
Average of a,b, and 2c = 153.
Whereas a=126 and b=135.
So, here we have a conclusion that the 2c value is more than 157 but the question is how much?
And the answer is 153-135 = 18.
And 153-126=27.
2c gave 18+27=45 to a and c then those values become 153
If 2c gives 45 to a and b it still has its average value of 153
If 2c gives 45 then, c gives= 45/2 = 22.50.
If c never gives that 22.50 to a and b to make an average value then the value of c was = 153 + 22.50 = 175.50.

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.

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.

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.

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.

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

@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.

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.

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.