Test: Alligation & Mixture (February 12) - CAT MCQ

Assume that a container contains x of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid

Hence milk now contained by the container = 40

► Since first and second varieties are mixed in equal proportions.So, their average price = Rs.
= Rs. 130.50

► So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

► Let x and (12-x) litres of milk be mixed from the first and second container respectively

► Amount of milk in x litres of the the first container = .75x

► Amount of water in x litres of the the first container = .25x

► Amount of milk in (12-x) litres of the the second container = .5(12-x)

► Amount of water in (12-x) litres of the the second container = .5(12-x)

► Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5

⇒ (.25x+6-5x)/(.75x+6-.5x) =3/5

⇒(6−.25x)/(.25x+6) =3/5

⇒30−1.25x=.75x+18

⇒2x=12

⇒x=6

► Since x = 6, 12-x = 12-6 = 6

Hence 6 and 6 litres of milk should mixed from the first and second container respectively

► Spirit in 1 litre mix of A = 5/7 litre.
► Spirit in 1 litre mix of B = 7/13 litre.
► Spirit in 1 litre mix of C = 8/13 litre. 
By rule of alligation we have required ratio X:Y

Therefore required ratio = 1/13 : 9/91
= 7:9

► Cost Price(CP) of Type 1 material is Rs. 15 per kg
► Cost Price(CP) of Type 2 material is Rs. 20 per kg
Type 1 and Type 2 are mixed in the ratio of 2 : 3

Therefore, rice per kg of the mixed variety of material = Rs.18

8 litres are drawn from a cask full of wine and is then filled with water.

This operation is performed three more times.

The ratio of the quantity of wine now left in cask to that of the water is 16 ∶ 65
Calculations:

Let the quantity of the wine in the cask originally be x litres.

After first operation, wine left in the cask = (x - 8) litres So, the ratio of the quantity of wine now left in cask to that of filled cask = 

This operation is performed three more times. Then, Wine : Water = 16 : 65 or wine : water = 16 : (16 + 65) = 81

Correct answer is 24.

By the rule of alligation we have 
► So ratio of 1st and 2nd quantities = 7:14
= 1:2
∴ Required quantity replaced = 2/3

► S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

By the rule of allilation, we have:

 Ratio of quantities of 1^st and 2^nd kind = 14 : 6 = 7 : 3.

► Let x kg of sugar of 1^st be mixed with 27 kg of 2^nd kind.

Then, 7 : 3 = x : 27

Thus, required ratio = 80 : 70 = 8 : 7