Question

A jar contain water and milk in the ratio 2 : 3. some milk is added in the jar who's amount is equal to 30% of water present in the jar. after this some water is added. whose amount is equal to 10% of quantity of milk present in the jar presently. what is the new ratio of water and milk in the jar?

Answer 1

Therefore the new ratio of water and milk in the jar is 9:1.

Step-by-step explanation:

Given that a jar contain water and milk in the ratio 2:3.

Let the amount of water in the jar be 2x

and the amount of milk in the jar be 3x.

Some milk is added in the jar for which the mixture equals to 30% of water present.

It means the ratio of water and milk = 30:70 = 3:7

Let y amount of milk is added in the jar.

According to the problem,

$\frac{2x}{3x+y}=\frac{3}{7}$

$\Rightarrow 7.2x=3(3x+y)$

⇒14x=9x+3y

⇒3y =14x-9x

⇒3y=5x

$\Rightarrow y=\frac53x$

The new amount of milk $=3x+\frac53x$

                                        $=\frac{9x+5x}{3}$

                                        $=\frac{14}{3}x$

After this some water is added whose amount is equal to 10% of quantity of milk present in the jar.

It means the ratio of water to milk = 10:(100-10)

                                                        =10:90

                                                         =1:9

Let z amount of water be added in the jar.

According to the problem,

$\frac{2x+z}{\frac{14}{3}x}=\frac{9}1$

$\Rightarrow 2x+z= 9\times \frac{14}{3}x$

⇒2x+z=42 x

⇒z=42x-2x

⇒z=40x

The new amount of water is =(2x+40x)

                                               =42x

Therefore the new ratio of water and milk in the jar is

$=42x:\frac{14}{3}x$

=126 : 14                 [ multiplying by $\frac3x$ ]

=9:1                         [ divided by 14]