Aptitude - Alligation or Mixture - Discussion

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.

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.

3.5, 1.5
Now, to make it easier, you can multiply both numbers by 10 to eliminate the decimal points:
3.5 * 10 = 35
1.5 * 10 = 15.

Next, simplify this ratio by dividing both numbers by their greatest common divisor (GCD), which is 5:
35/5 = 7
15/5 = 3
(/5 is the greatest common divisor)
So, the final simplified ratio is 7:3.
So, the final simplified ratio is 7:3.

The mean price is a trick , this question is particularly based on it . as we see there is only one equation made i.e [15x + 20y = 16.5] other than this we cant make any equation.

My suggestion to solve these type of question where only one equation is made to put the value of options given.

As here only one option satisfies.

Let x kg of 1st is taken and (1-x) of 2nd is taken.

Then price of mixture will be:15*x+20*(1-x)=20-5x ----(1)

Given price of mixture is 16.5 -----(2)

From Equation (1) & (2)

20-5x=16.5

=> 5x=20-16.5
=> x=3.5/5
=> x=0.7

So,ratio is x:1-x i.e. 0.7:0.3 => 7:3 ans

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.

Its better to follow simple method boss.

Lets assume that price of A be 150 and B is 200.
Mixture to sell at 165.

Cheaper grocery profit = 165-150 = 15.
Dearer grocery loss = 200-165=35.
Ratios to sell at 165 is.

35
---- = 7:3
15

(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.

Let the ratio be x:y.

Suppose x kg of pulse1 and y kg of pulse2 is mixed. The total kg of the mixture will be (x+y)kg.
So, equating the costs:
15x+20y=16.5(x+y).
1.5x=3.5y.
So, x/y=3.5/1.5.
->x:y=7:3.

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.