Latest Accenture Aptitude Question SOLUTION: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once

ans: 9:1
Initially ixture has milk and water in ratio of 12:8.
when 10 ltr of mixture is removed , left mixture has milk and water in qnty/ratio of 6:4.
when 10 ltr milk is added , ratio becomes, 16:4, ratio is now 4:1
now milk is 8 lt and water is 2 lt in 10 lt mixture
again replaced by 10 lt of milk hence milk and water is in 18:2 in 20 lt mix
so ratio becomes 9:1

he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.

Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.

Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.

Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore, "W_r ={W_o}/4= 8/4 = 2 litres

Reference: http://www.lofoya.com/Aptitude-Questions-And-Answers/Alligation-or-Mixture/l3p1.htm

3:17

Initiall ixture has milk and water in ratio of 12:8.
when 10 ltr of mixture is removed , left mixture has milk and water in qnty/ratio of 6:4.
when 10 ltr water is added , ratio becomes, 6:14
when again 10 ltr of mixture is removed , left mixture has milk and water in qnty/ratio of 3:7
when again when 10 ltr water is added , ratio becomes, 3:17

First Iteration solve
Before-
m=(3/5)*10=6 and w=10-6=4

After-
m=6+10=16 and w=4
now Ratio=16:4=4:1

Second iteration solve

Before-
m=(4/5)*10=8 and w=10-8=2

After-
m=10+8=18 and w=2

now final ratio=18:2=9:1

The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.

Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step.

Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.

Shortcut.
We are essentially replacing water in the mixture with pure milk.

Let WoWo be the amount of water in the mixture originally = 8 litres.
Let WrWr be the amount of water in the mixture after the replacements have taken place.

Then, WrWo=(1−RM)nWrWo=(1−RM)n
where, RR is the amount of the mixture replaced by milk in each of the steps, MM is the total volume of the mixture and nn is the number of times the cycle is repeated.

Hence, WrWo=(12)2=14WrWo=(12)2=14

Therefore, Wr=Wo4=84=2Wr=Wo4=84=2 litres

Hence, the mixture will have 18 litres of milk and 2 litres of water.

Therefore, the ratio of milk and water is 18 : 2
9 : 1 Ans.