# Difficult Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
 ✔ A. 5 litres ✖ B. 7 litres ✖ C. 10 litres ✖ D. None of these

Solution:
Option(A) is correct

30 litres of the mixture has milk and water in the ratio 7 : 3. i.e. the solution has 21 litres of milk and 9 litres of water.

When you add more water, the amount of milk in the mixture remains constant at 21 litres. In the first case, before addition of further water, 21 litres of milk accounts for 70% by volume. After water is added, the new mixture contains 60% milk and 40% water.

Therefore, the 21 litres of milk accounts for 60% by volume.

Hence, 100% volume $=\dfrac{21}{0.6} =35$ litres.

We started with 30 litres and ended up with 35 litres.

Therefore, 5 litres of water was added.

Edit: For an alternative solution, check comment by Vaibhav Gupta.

Edit 2: For yet another alternative solution, check comment by K Sainath.

## (7) Comment(s)

Jitendra
()

suppose x litres of water mixed. Now take the ratio of water with mixture

: (30*(3/10)+x)/(30+x)=40/100

by solving this you will get x=5.

K Sainath
()

As 30 litre of mix having $\text{milk:water}=21:9$

Let, new water be $x$

Then $\dfrac{(x+9)}{21}=\dfrac{40}{60}$

By solving we get  $x= \textbf{5 litre}$ that is to be added.

Vaibhav Gupta
()

Alternate solution:

$7:3$ means it has 21l milk and 9l water

Let $x$ litre water is added then total mixture $= 30+x$

As 40% must be water so 60 % must be milk

Therefore,

$\text{60% of } (30+x) = 21 \text{ litre}$

By solving it we get,

$x=5$

Thus, 5 litres of water must be added

Dhondu
()

Good question. Keep doing the good job.

Hassini
()

i cant understand tell clearly

Wsedrftgyh
()

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Vaibhav Gupta
()

See my solution that would be helpful