mixture and solution problem?

Question

A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%.

MYSol : 10% = 10/100 = 1/10 = 2/20 i.e 20kg of solution contains 2 kg of water so the actual spirit content is 20 - 2 = 18 kg.

now 25% of 18 is 4.5 so if we add 4.5 kg of water to 18kg of spirit the solution becomes 25% water.

So now actual amount of water to be added is 4.5 - 2 = 2.5 to make the solution 25% water.

But the actual answer is 4, i am not sure where i am wrong.

Answer 1

If you add 2.5 k then you have 4.5 k in a total of (18 + 2 + 2.5) = 24.5 k so that you end up with 4.5 / 24.5 = ~18.4% water.

If x is the amount of water you add, you need to solve the equation (2 + x) / (18 + 2 + x) = 0.25

Give it a try: I'll add the answer later if you're still stuck.

Answer 2

Let's call the amount of water you have at the end $x$. Currently, as you mentioned, we have 2 kg of water, and 18 kg of the mixture. The mixture will stay constant because we're only adding water.

We need to model the total weight when some amount $x$ of water is present. It's very simple, it will just be:

$$w=18+x$$

The weight of the mixture and the weight of the water will together be the total weight.

Now we want to know when the weight of the water will be 25% of the total weight. Well, this literally means that $$x=0.25w$$

Cool! Now we can plug it in: $$4x=18+x$$ I plugged in $w=4x$ because we're solving for $x$, but it doesn't matter if you solve for $w$ and then plug it in to get $x$.

Now solve for $x$: $$3x=18$$ $$x=6$$

Therefore, the amount added is: $6-2=\therefore 4$

Answer 3

Let us consider that water is $2$ kg and spirit is $18$ kg,according to given details.

Now what we will do to leave the water and take the spirit under calculation.

So in $20$ kg mixture, it was $18$ kg spirit, i.e. $90\%$, and the amount of spirit is constant but turns to $75\%$, so our calculation will go like

Let the final quantity of mixture be $x$; $75\%$ of $x = 18$. After solving, $x = 24$, i.e. our final quantity of mixture. So from here, we can conclude that the water added will be $24-20= 4$ kgs.