Aptitude - Alligation or Mixture - Discussion

Let there be 8 liters of solution, in which 3/8 liter be water and 5/8 lt be syrup. As we can see syrup is more than water so of course some syrup is to be replaced with water. As it is a solution and we can't remove only syrup or water so we have to remove the whole solution and replace it with water.

Now using ratio and proportion (5-(5x/8))/(3-(3x/8)+x) = 1/1.

As some part of syrup will be removed we also have to remove water as i have told that we are replacing some part of whole solution with water thats why we are subtracting 5x/8, 3x/8 from numerator and denominator respectively, now after removing solution we have add equal quantity of water thats why we will add water in denominator which will be equivalent to the quantity of the solution removed i.e 5x/8+3x/8=x. On the RHS side value will be as we want both the syrup and water in same proportion i.e 1/1.

1. Let volume of vessel be x.

Now the ratio is 3:5 initially.
(3/8)x water and (5/8)x syrup.

2. Now let y liter of mixture drawn off.

Means now {(3/8)x - (3/8)y} water and {(5/8)x - (5/8)y} syrup in remaining mixture.

3. Now y liters of water mix to make the equal quantity of both water and syrup,

Then, 3/8(x-y)+y = 5/8(x-y),
y = 1/5x.

What is the another way to solve this problem even more easier?

Can anyone solve this equation for me?

3-3x/8+x = 5-5x/8

Let there be 1kg of mixture with water concentration 3/8 i.e. 3/8 kg water present.

X kg mixture is removed so water removed = 3X/8.

Now X kg pure water is added.

In the required mixture water = 1/2 kg. So balancing over water.

3/8 " 3X/8 + X = 1/2 solving we get X = 1/5.

Easy solution :

3 parts + 5 parts = 8 parts.

For equality (3+1) parts + (5-1) parts = 4 parts (equals).

Hence we need to reduce 1 part that will be from 5 parts.

Hence : 1 (part)/5(parts) is reduced.

Hope you understand.

Can anybody gives the easiest way of solving it?

Concentration = a(1 - y/x)^n.

Remaining Syrup/Total volume = Concentration.

a = contamination of original solution, here in this case is 3:5 Viz 3/8.

Since water is 3 parts and syrup is 5 part that means the solution is contaminated with 37.5% in terms of syrup.

Now, Concentration = 1/2 (since, 50 % solution is desired).

Therefore, Using the above formula,

1/2 = 3/8(1 - y/x).

Here y = quantity of mixture drawn off.
x = initial volume.

We don't know either so leave it as it is. Solving we get,

Y/x = 1/4.

Now, Y:x::1:4.

Therefore, y = 1/1+4 = 1/5.

i.e 1 part of solution has been drawn off for per 5 part of the solution.

How is the equation solved?

i.e. How do we get, 5x+24? Can anybody explain?

To make equal parts, we just take 1 part from syrup and replace with water to get 4 parts of water and 4 parts of syrup.

So we are replacing 1 part of syrup of 5 parts with water, so the answer is 1/5.