Aptitude - Alligation or Mixture - Discussion

8/5 * 1/8 is done because part of the mixture has to be replaced.

Since a part of the mixture is 1/8, the final answer is multiplied with it.

Attention to those who want to understand the solution provided with the question.

Suppose the vessel initially contains 8 litres of liquid. ------> vessel contains => 8l mixture.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = 3 - (3x/8) + x litres.

------ >[3lit water it originally contained] - [ (3x/8) l water which was removed when you removed 'x' l mixture] + ['x' litre water that you added].

Hope that'll justify the remaining solution too.

WATER : SYRUP

3 : 5 = 8.
2 : 0 = 2 (TO BOTH BECOME EQUAL ADD 2 UNITS TO WATER).
5 : 5 = 10 (RATIO IS EQUAL NOW).

SO, ADDED AMOUNT OF WATER IS 2/10 OF FULL AMOUNT. IF YOU SIMPLIFIED IT'S 1/5.

Assume we have 80 liters of the solution. Then, we will be having 30 liters of water and 50 liters of syrup.
Let x be the % of water that we have to add to the solution, to increase the % of water to 50%.
30 + x/80 + x = 1/2.
=> x = 20.

Nice explanation @Victor.

Let water be 0.6 L whereas syrup is 1L.

0.6 + 0.2 = 0.8 : 1 - 0.2 = 0.8
1 : 1,
0.2/1=1/5.

(Here, to solve the problem without complex one thing is to have it in our mind that is what amount of water is taken from a mixture which is filled with the same amount of water again. Thus how much amount of syrup is drawn off from the mixture that is taken in our consideration then 0.2/1 = 1/5 is answer.

W:S = 3:5 after adding water it become 1:1 here there is no change in syrup so multiply 5 * (1:1) = 5/5 so only water is change 2 part now 2/(5 + 5) = 2/10 = 1/5.

@Murali.

Here I want to add something regarding your confusion about the last step.

For eg, if we say 2 is what part of 8? Ans is 1/4 and how? ( 2 / 8 = 1/4 )

Similarly 5/8 is what part of 8? Ans is ( (5/8) / 8) i.e (5 / 8) * 1/8 = 1/5.

Quantity of syrup is 5. Quantity of water is 3. You have to add and subtract 1 from water quant and syrup quant respectively. Keep that one in numerator and the amount of which has to be reduced (syrup 5) should come in the denominator. 1/5. I have tried with other problems also it worked.

It is simple as Kiran said. Suppose you have total (means 100% solution) is 8 litre. In which you have 5 parts of milk means 60% milk and 3 parts of water means 40% water. Now you have to make mixture 50%-50%. So you have to reduce 10% milk and increase 10% water means if you mix 20% extra water in that then it will reduce quantity of milk 10% and increase water 10% in solution. That's it answer is 20% = 20/100 = 1/5.