Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.15)

15. 

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

[A]. 400 kg
[B]. 560 kg
[C]. 600 kg
[D]. 640 kg

Answer: Option C

Explanation:

By the rule of alligation, we have:

Profit on 1st part Profit on 2nd part
8% Mean Profit
14%
18%
4 6

Ration of 1st and 2nd parts = 4 : 6 = 2 : 3

Quantity of 2nd kind = 3 x 1000 kg = 600 kg.
5


Target said: (Nov 20, 2010)  
From where this 4 and 6 comes? I din't get it.

Priya said: (Nov 29, 2010)  
@target

18-14=4
and
8-14=6

hope it helps u..

Ajith Kumar said: (Jul 19, 2011)  
Thank you, I was also suffering with same doubt. It helped me a lot.

Hjgh said: (Jul 24, 2011)  
Thanks helped me a lot.

Nikunj Patel said: (Aug 2, 2011)  
From where did this 3/5 come?

Kishore said: (Sep 9, 2011)  
Here the second part ratio is 3 and total mixture part is 5 so it came as the ratio 3/5.

Karthi said: (Jan 5, 2012)  
Where did 3/5 come ?

Vasumaila said: (May 1, 2012)  
The ratio of 1st & 2nd = 4:6=2:3
so its become 2+3=5
so we calculate 3/5*1000=600

I hope U understand

Simit said: (Aug 3, 2013)  
Let us consider 2 part X(18%)&Y(8%).

Now 1000-x = y.

1000*1.14 = x*1.18+y*1.08.

1000*1.14 = x*1.18+(1000-x)1.08.

1000*0.06 = x*0.1.

x = 600.

Kanna said: (Jul 1, 2014)  
How 3/5 is coming ?

Rajesh said: (Jul 7, 2014)  
Yes its suggest how you found 3/5?

Math_Lover said: (Jul 10, 2014)  
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 :).

Himanshu said: (Aug 7, 2014)  
In allegation formula we put the cost price, but here we are putting the selling price, why?

Robin said: (Aug 30, 2014)  
@Himanshu.

Basically, the allegation formula is deployed w.r.t unit of mean quantity, not specifically on cost price, which is profit% in this case.

Sarath said: (Nov 20, 2014)  
Why we have to do 18%-14% and 14%-8% and put it on right left?

Anjali said: (Apr 14, 2015)  
@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?

Gokul said: (Sep 1, 2015)  
If 18-14 = 4 and 14-8 = 6.

Then the ratio must be 3:2 for a:b how come it is 2:3?

Madhav Kudikyal said: (Sep 3, 2015)  
Thanks it just cleared my doubt.

Krishna Rathi said: (Jan 16, 2016)  
Any alternative way to solving this question?

Nidhi said: (Mar 15, 2016)  
Suppose x part is for 8% and y is for 18% then,
x+y = 1000.

8x+18y = (x+y)14.
x/y = 2/3.
y = 3/5*1000.
y = 600.

Pikot said: (Mar 17, 2016)  
1500 is my answer. Why. Is there a formula?

Thiru said: (Apr 22, 2016)  
@Kanna & @Rajesh.

3 is the 18% number and 5 means 2 + 3 = 5.

Saranya Kumar said: (Jul 26, 2016)  
118x + 108(1000 - x) = 114000.
59x + 54(1000 - x) = 57000.
5x = 3000.
x = 600.

Timo said: (Sep 29, 2016)  
@ 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?

Pooja said: (Nov 23, 2016)  
How to solve if the merchant is in the loss for the 2nd time?

Gobi said: (Dec 12, 2016)  
Why in this place taking selling price?

Ritija said: (Mar 14, 2017)  
Why we calculate the second part only?

Please tell me.

Naveen Kumar said: (May 21, 2017)  
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.

Abhi M said: (Jul 14, 2017)  
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?

Chinki said: (Jul 30, 2017)  
Why 2/3 is not multiplied by 1000?

Asha said: (Aug 23, 2017)  
@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.

Aditya said: (Aug 30, 2017)  
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?

Lucky said: (Oct 9, 2017)  
Thank you all.

R.Jaswanth Raju said: (Oct 31, 2017)  
@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.

Shree said: (Feb 20, 2018)  
Thank you all for explaining the solution.

Ananda said: (Apr 27, 2018)  
Clear explanations. Thanks for your great help.

Mohan said: (Jun 9, 2018)  
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.

Chanukya said: (Aug 1, 2018)  
Thank you helped me.

Yogesha said: (Dec 20, 2018)  
How to calculate 1st ratio and 2nd ratio? Please tell me.

Marvi said: (Mar 15, 2019)  
How to calculate 1st nd 2nd ratio?

Nafiul said: (Nov 27, 2019)  
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.

Andy said: (Apr 5, 2020)  
8x + 18(1000-x)/x+1000-x =14.
8x+18000-18x = 14000,
Solving x you get 400,
1000 - 400 = 600.

Gokul Ramakrishnan said: (Apr 30, 2021)  
Thank you it helped me a lot.

Manish said: (Oct 1, 2021)  
14-8 = 6.
18-14 = 4.

Ratio of 1st = 2:3.

Now;
2+3 = 5,
5 units = 1000,
1 units = 200, then
3 units = 3*200 = 600.

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