Aptitude - Alligation or Mixture - Discussion

Before going to shortcuts I explain some known facts about this question.

1. Only water is added and no effect on syrup.

2. So think like how much water is added so that mixture is 1:1.

Lets start my shortcuts:

Water:Syrup 3:5.

After mixing water 1:1.

We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5.

Finally we see:
Before 3:5.
After 5:5.

Clearly we see that two part of water is added.

Hence amount of water added as new solution is gives answer.

2/10 = 1/5.

Trick is based on how much you think and how much you understand.

I don't understand none of the method above said. Can anyone tell mathematically?

@Anand shaw.

Your method is good. But last passage after 4:1 can you elaborate more?

Water in one mixture : 3/8.

Water in another mixture : 1.

Water in new mixture : 1/2.

According allegation formula:

Ratio of quantity of two mixtures mixed : (3/8-1/2) : (1-1/2) = 4:1.

So 1/5 parts of another mixture is mixed with one.

Another mixture is pure and is same as mixture replaced.

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.

How is the equation solved?

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

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.

Can anybody gives the easiest way of solving it?

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.

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.