# Easy Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. In a 729 litres mixture of milk and water, the ratio of milk to water is 7:2. To get a new mixture containing milk and water in the ratio 7:3, the amount of water to be added is:
 ✖ A. 51 litres ✖ B. 61 litres ✖ C. 71 litres ✔ D. 81 litres

Solution:
Option(D) is correct

Quantity of milk in 729 litre of mixture,

$= \dfrac{7}{9}\times 729 = 567$ litre

Quantity of water,

$= 729-567 = 162$ litre.

Let $x$ litre of water be added to make ratio $7:3$.

Milk                water
$567$              $(162+x)$
\           /
mixture
$(729+x)$
/           \
$567$     :     $(162+x)$
$7$        :           $3$

$\Rightarrow \dfrac{7}{3} = \dfrac{567}{162+x}$

$\Rightarrow 162\times 7 + 7x = 567\times 3$

$\Rightarrow 7x = 1701-1134 = 567$

$\Rightarrow x = \dfrac{567}{7}$

$= \textbf{81 litre}$ water is to be added.

Edit: For an alternate solution ( a quick one), do check KARTIK's comment.

Edit 2: For yet another shortcut alternate solution, check comment by Rajat Srivastava.

## (8) Comment(s)

Hazarath
()

7+2=9 parts

729/9=81

now 7+3=10 parts

for 10 parts add one extra 81.

Deepak
()

Ratio 7:2 gives 567 part milk ie 7 part.

So 1 part milk=567/8=81.

Increse in water is 1 part ..so amount of water added is 81.

Indra Kiram
()

milk:water :- 7: 2; Milk:-567, water:-162,let water added be X. In new solution Milk:- 567, Water: 162+x, Total solu:-729+x and ratio is 7:3

simply $7/10(729+x)=567$, upon calculation we get X =81.

Himal Hazra
()

7:2 ratio hence 7/9 * 729 = 567 rest is water 729-567=162 what must be added to water to have ratio 7:3

567/(162+x) = 7/3

x = 81 ltrs ans

Rajat Srivastava
()

2 units out of a total 9 constitute water with a total of 729 litres.

Therefore 1 unit of water $= (\frac{2}{9}) \times 729 = 81$.

In the new solution, water is 1 unit more and the amount of milk remaining same.

Units of water added $(3-2) = 1$ unit

$= \textbf{81 litres}.$

Sandeep
()

What if the new ratio to be obtained is 8:5?

Math
()

Since only water is added, milk quantity remains same, 567ltrs. Now final mixture ratio 8:5, do 8parts=567;

therefore

5parts= 567*5/8s

KARTIK
()

milk:water $= 7:2$

Amount of milk $= 7x$

Amount of water $= 2x$

Total amount of mixture, $7x + 2x = 9x=729$

$\Rightarrow x=\dfrac{729}{9} = 81$

So, for every increase in ratio there is increase of 81

Now Ratio has been changed from $7:2$ to $7:3$ which is an increase in the ratio by 1, so 81 litres of water is to be added.

Now taking it forward,

If final ratio were $7:5$, (increase of ratio by 3)

Then increase would be $81*3=243$