Aptitude - Alligation or Mixture - Discussion

Can we able to solve this problem in alligation method, if so explain?

Ratio given is 3:5 (AS 3 Part water & 5 part syrup).

Take even LCM of 3 & 5 i.e. 24, 30 etc.

Suppose we take 24 as LCM.

Now divide LCM by 8 (addition of ratios i.e. 3+5).

So, 24/8=3.

Now, multiply both the terms of ratio by 3.

So we get 9 (water) and 15 (syrup).

As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.

So we get 3/15= 1/5.

Let volume is 8.

Water = 3/8 syrup = 5/8.

According to question,

Suppose y mixture(water,syrup)are drawn.

Water quantity is 3y/8 and syrup quantity is 5y/8.

3/8-3y/8+y = 5/8-5y/8.

y = 1/5.

It is a common sense.

Finally in the solution 50% syrup & 50% water will remain.

That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.

=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.

A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20% litres of the first solution to make a solution of 10% sugar?

I think the issue with some of the guys here is they find these mathematical theories hard to understand. Let me make it simpler for them.

They didn't give the volume of vessel in the question so never mind that. The vessel contains 8 parts of liquids (i.e. - 3 parts of water and 5 parts of syrup).

What they are asking is to make the mixture into half water and half syrup i.e. - 4 parts of water and 4 parts of syrup. To make it happen you need to take 1 part of syrup out of the vessel (which is 1/5th of the total syrup) and add 1 part of water instead and thus you get the answer 1/5!

@Kiran how you got 60% and 40%

If I do - (3/8)*100 it gives 37.5%, How you got 60 and 40?

Thanks @Kousik Maji for your good solution but I am confused with bellow sentence please give clear cut info.

1/8 ........................(8/5)X(1/8)=1/5.

Here total mixture is(3+5)=8.
Now syrup=5/8 and water=3/8.

If we take some mixture and added same amount of water then amount of syrup will be 1/2 and water 1/2.

Now the amount of syrup present in removed mixture is 5/8-1/2=1/8.

Now 5/8 syrup present in mixture 1.

1/8 ........................(8/5)X(1/8)=1/5.

Here given 8 parts of total, 3 parts water &5 parts syrup. Then we equal the both water & syrup ratio. Now we add the 1 part of syrup from 5 parts of syrup i.e;1/5 then it will become equal parts of water & syrup.

The answer is:1/5.