Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.11)

11. 

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

[A]. 1 : 3
[B]. 2 : 3
[C]. 3 : 4
[D]. 4 : 5

Answer: Option B

Explanation:

By the rule of alligation:

Cost of 1 kg of 1st kind Cost of 1 kg of 2nd kind
720 p Mean Price
630 p
570 p
60 90

Required ratio = 60 : 90 = 2 : 3.


Ajay said: (Jun 18, 2011)  
How 60 & 90 came here?

Chirag said: (Jul 1, 2011)  
@Ajay

630 - 570 = 60 and
720 - 630 = 90

It is simple.

Angeeta said: (Dec 15, 2011)  
According to the formula the cheaper price is came frist and bearer price is second. so according to me the answer is 90:60=3:2
am i right?

Nitin Gusain said: (Feb 15, 2012)  
Yes @Angeeta according me you are right.

I think it is a mistake.

It should be 90:60 or 3:2.

Varun Kumar said: (Feb 18, 2012)  
Rule of Alligation : If two ingredients are mixed, then :

c = Cost price of a unit quantity of cheaper

d= C.P. of a unit quantity of dearer



(Quantity of Cheaper) / (Quantity of dearer) = {(C.P. of Dearer) - (Mean price)} / {(Mean Price) - (C.P. of Cheaper)}


(Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c)


c d
\ /
\/
/\mean price (m)
/ \
(d-m) (m-c)

Hari said: (Feb 26, 2012)  
How 630 came?

Vasumaila said: (May 1, 2012)  
worth of cost=6.30
so 6.30*100=630

den

720-630=90
630-570=60
so
90:30=2:3

Sakshi said: (Aug 24, 2012)  
According to books cheaper price shoul b taken firtt then dearer. So I think answer is 3:2. Please clear my doubt m I right?

Oldman said: (Oct 1, 2012)  
Let the ratio be x/1-x
Then
7.20 (1-x) + 5.70 x = 6.30
7.20 -7.20x + 5.70x =6.30
7.20-1.50x =6.30
7.20-6.30 /1.50 =x
0.90/1.50 = x
3/5 =x
1-x = 1-3/5 =2/5
x/1-x = 3/5 /2/5 = 3/2

Vaishnavi said: (Jul 12, 2014)  
No its 2:3 only.
How it comes is that,

-> (6.30-7.20)=> -0.60.
-> (5.70-6.30)=> -0.90.

Upon equating them acc to allegations rule, you get,
0.2:0.3 which will be 2:3;

I guess it comes this way..am I right?

Pushpa said: (Jan 23, 2015)  
Rule of alligation we will get 3:2 (Cheaper quantity: Dearer quantity) as answer but in question it asked the ratio of dearer qty to the cheaper one tats why answer will be 2:3 hope I have made my point clear!

Pushpa said: (Jan 23, 2015)  
Guys following rule of alligation we will get 3:2 (Cheaper quantity:Dearer quantity) as answer but in question it is asked the ratio of dearer qty to the cheaper one tats why answer will be 2:3 hope I have made my point clear!

Sumanth Geras said: (Jul 21, 2015)  
7.20(x)+5.70(y)/x+y = 6.30.

Here x and y are the ratio's in which they are mixed.

7.20(x)+5.70(y) = 6.30(x)+6.30(y).

On solving we get x:y = 2:3.

This is the easiest method for these kind of problems.

Jas said: (Feb 11, 2016)  
As per alligation rule they have written in wrong order.

Mazhaurl91Bd said: (Feb 11, 2016)  
Details solution:

Let, X kg mixture with take 7.20 and 1 kg mixture with take 5.70.

Then, Cost price of 1 kg mixture is (7.20x + 5.70)/(x+1).

According to the question:

(7.20x + 5.70)/(x+1) = 6.30.

=> 7.20x + 5.70 = 6.30x + 6.30.

=> 0.90x = 0.60.

=> x = 2/3.

Ashok said: (Jun 30, 2016)  
No, this answer is wrong because it contains cheaper quantity on the left side and higher quantity on other side but in this solution, it is appearing on opposite side according to the rule of alligation.

Its kind of star problem conducted by some corporate company to check that canditate's are guessing.

Mahi said: (Jul 6, 2016)  
Hello, According to alligation rule the answer is wrong. But I referred some books, I came to know that when in the question we gave the same kind of products like (first kind of rice and second of rice as given in the above question).
We should take the allegation rule as per question sequence.

In the above question, we have the highest value 7.20 first followed by 5.70. So we should take 7.20 first in alligation rule.

Hope my answer is helpful.

Deepti said: (Aug 10, 2016)  
Thank you, your explanation was helpful.

Sai said: (Aug 19, 2016)  
Thank you all for the explanation.

Siva said: (Aug 26, 2016)  
Actually, the alligation formula.

Cheaper price dearer price.
Mean price.

From this formula, 720 itself come first. So the answer is 3:2.

Pradeep said: (Oct 8, 2016)  
No the answer is correct ,though it does not use the standard alligation formula.

Reverse work the answer
2/5th of 1 kg of mixed rice = 0.4 kg of 1st variety @ Rs 7.2/Kg dearer ricee.
3/5th of 1 kg of mixed rice=0.6 kg of 2nd variety @ Rs 5.7/Kg cheaper rice.
Therefore the sum of cost price of individual component as per the ratio mixture must be equal to cost price of 1kg of the mixture
(7.2 * 0.4) + (0.6 * 5.7) = 6.3.

Also no option of 3:2.

Pratap Chandra Das said: (Jan 29, 2017)  
I think the answer is correct.
2 parts of 720 + 3 parts of 570.
=> 2 * 720+3 * 570 = 3150.
Per kg rice(i.e.,mean price)= 3150/5 = 630.
{hear 5 is 2:3}
2:3 is correct instead 3:2.

Shruti said: (Mar 1, 2017)  
No cheaper quantity is mixed in more amount so answer is 2 : 3.

Pravat Sahu said: (Apr 6, 2017)  
How 630 came? Please explain me.

Manuadhish said: (Oct 28, 2017)  
Use weighted average= 7.2x+5.7y/x+y=6.3,
On solving we get x/y=2/3.

Shree said: (Feb 20, 2018)  
Thanks for the explanations.

Ravi said: (Aug 29, 2018)  
How 90:30 come?

Bargavi said: (Aug 9, 2020)  
Correct, Thanks @Pushpa.

Sony Tiwary said: (Sep 15, 2020)  
Yes, the correct answer is 3:2.

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