Aptitude - Alligation or Mixture - Discussion

Let x part is sell with 8% profit
And the rest 1000-x with 18%
And total profit is 14%.

Then we can write;

(X * 8) (1000-x)*18 (1000 * 14)
---------------- + ----------- = ------------------
100 100 100

Here all 100 in the denominator is cancel out;
And we get,
8x + 1000*18 - 18x = 1000*14
-10x = 14000 - 18000
-10x = -4000
X = 400.

The quantity sold at 18% profit is:

1000 - x = 1000 - 400 = 600 Ans.

I HOPE IT WILL HELP TO MAKE WITH BASIC WITHOUT ALLIGATION METHOD.

THANK YOU.

@Sarath. As you are mixing with each of its kind so. The allegation formula suggests us to subtract the cheaper from the mean and to subtract the dearer from the mean. The resultant is the C.P of the mixtures. Is it now clear to you?

@ Simit.

I'm really trying to follow your explanation, its quite easy for me than the other methods. But I'm lost along the way, why multiply 1000 which is the total quantity by the 1.14 which is the percentage increase in profit?

@Chinki

Because they have asked only about the quantity which is sold for 18% profit
if they asked to fine out the quantity which is sold for 8% profit you can multiply 2/5 (bcs 2/(3+2)) with 1000.

=(2/5) * 1000 => 400kg.

Because they asked to find about 2nd one only.observe the allegation rule the no below 18% is 6. So that must be calculated .the ratio is 4:6 it means that (6/10) * 1000 = 600.

We get the answer. Hope you got it.

A businessman sells some sugar in total sugar of 50 kg on 8% profit and remaining sugar on 18% profit. If the average profit is 14%. Find the amount of sugar which was sold on 18% profit.

Can anyone solve this?

@Aditya.

Just like the above question we can apply same rule and method to solve your question.

ANSWER:

He sold 30kg sugar for 18% profit.
After solving we get 4:6=>2:3
3/5*50 = 30.
Here 30 indicates kgs.

Ql=Quality of Lower.
Qh=Quality of Higher(Let x).
Pl=Profit of Lower.
Ph=Profit of Higher.

Ql/Qh=(Ph - M)/(M - Pl).
(1000-x)/x=(18-14)/(14-8).
(1000-x)/x=4/6.
(1000-x)/x=2/3.
2x=3000-3x.
5x=3000.
x=600.

The ratio is 2:3 which means 2 parts of 1st type and 3 parts of 2nd type and total of 1st and 2nd type is 5 parts.

Taking the fraction of 2nd type of sugar to total amount, we get 3/5 :).

Hey Guys,

I have a question.

When the quantities are all expressed in percentages, can we take the values as it is? Without having to find out the Cost Prices or Selling Prices?