Aptitude - Alligation or Mixture - Discussion

Let x=15,y=20.
We know that x+y=16.50.

We can write in eqtion form:

15x+20y = 16.50(x+y)
16.50x-15x = 20y-16.50y
1.50x =3.50y
x/y = 3.50/1.50

Just we can convert

From eq x = 350/100=35
Eqtion y = 150/100=15

There fore ratio is
x:y =35:15.

Then answer is 7:3.

@Atul.

Really superb solution. Unlike the theoretical approach this is quite simple to understand.

Let x kg first variety mixed with y kg of second variety.

So total cost of(x+y) kg is Rs. 15x+20y.

So cost of 1 kg mixture is Rs. (15x+20y)/x+y.

Now according to question,

(15x+20y)/(x+y)=16.50
=> (15x+20y)/(x+y)=33/2
=>33x+33y=30x+40y
=>3x=7y
=> x:y=7:3.

Answer is 7:3.

Check the option first.

7:3 = 7*first variety/10 + 3*second variety/10 = 16.50.

7*15/10 = 10.5.

3*20/10 = 6.

By adding two you'll get 16.5.

So 7:3 is correct.

In the question Rs 15 and Rs 20 are mentioned the prices of 1st and 2nd varieties sequentially so we need to take Rs 20 -16.50 as the first variant in the solution.

Is the below mentioned method correct.

15/2 = 7.5( consider it has 7).
20/2 = 10.
10-7 = 3.

So the answer is 7:3?

There is a shortcut to solve such ratio questions.

1. Take the difference between the average value and the next quantity value. similarly, take the difference between the average value and the first told quantity.

So, here it is 20 -16.50 i.e. 3.50
Now, for the first quantity it is 16.5 - 15 i.e. 1.50

Now, the ratio is 3.5 /1.5 i.e. 7:3.

My question here - I understand from the equation formation that by taking such differences I will get the answer.

However, my question is to understand visually this process of solution. How come a difference gave us the right ratio? Is there any hidden fundamental behind it? Can someone decipher this difference technique via. Singapore Maths? Why difference gave me the answer is what I am puzzled. Please don't explain me from the equation point of view.

How 3.50 and 1.50 come?

(20-16.50)=3.50.
(16.50-15)=1.50.

If values in points means should divide by 100 or 10 based on that because ratio should not be in points. So,

3.50/100 = 35.
1.50/100 = 15.

Respectively 35:15 = 7:3.

=3.50/100= 0.035.
& 1.50/100 = 0.015.

How 3.50/100 = 35., 1.50/100 = 15.?