Aptitude - Alligation or Mixture - Discussion

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)

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.

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.

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.

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.

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!

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?

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!

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.

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.