Question

9. A container is filled with liquid, 6 part of which are
water and 10 part milk. How much of the mixture
must be drawn off and replaced with water, so that
the mixture may be half water and half milk ?​

Answer 1

Step-by-step explanation:

${\Large{\mathbf{\underline{\underline{\red{Question :}}}}}}$

A container is filled with liquid, 6 part of which are water and 10 part milk. How much of the mixture must be drawn off and replaced with water, so that the mixture may be half water and half milk ?

${\Large{\mathbf{\underline{\underline{\red{Solution :}}}}}}$

➠ Let the container initially contains 16 L of liquid

➠ Let's take L be the compressing liquid

✯ Quantity of water in the new mixture :

${\bold{\sf{: \: ⟹ \: \: \: \: \: \Big( 6 \: + \: \frac{6a}{16} \: + \: a\Big ) \: \: L}}}$

✯ Quantity of milk in the new mixture :

${\bold{\sf{: \: ⟹ \: \: \: \: \: \Big( 10 \: - \: \frac{10a}{16}\Big) \: L}}}$

According to the question,

${\bold{\sf{: \: ⟹ \: \: \: \: \: 6 \: + \: \frac{6a}{16} \: + \: a \: \: = \: \: 10 \: - \: \frac{10a}{16}}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 96 \: - \: 6a \: + \: 16a \: = \: 160 \: - \: 10a}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 96 \: + \: 10a \: = \: 160 \: - \: 10a}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 20a \: = \: 64}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: a \: = \: \frac{64}{20}}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: a \: = \: \frac{16}{5}}}}$

Therefore,

The part of mixture replaced :

${\bold{\sf{: \: ⟹ \: \: \: \: \: \frac{1}{16} \: × \: \frac{16}{5}}}}$

$: \: ⟹ \: \: \: \: \: {\bold{\mathrm{\boxed{\pink{ \: \: \: \: \: \frac{1}{5} \: \: \: \: \: }}}}}$

Answer 2

Answer:

Given : 6 part is water and 10 part is milk.

Find : Part of mixture to be drawn off and replaced with water  

so that the mixture would have equal water and milk.  

Let the part of mixture to be drawn off and replaced with water be x.

The water milk ratio in the liquid is 6:10.

New ratio=1/1

So what we are doing is taking out the milk according to the mixture ratio and adding that much of water to the mixture.

Amount of water added=Amount of milk taken out=(x/16)10.

⇒((x/16)10+6)/(10-(x/16)10)=1/1

⇒(x/16)10+6=10-(x/16)10  

⇒(x/16)20=4  

⇒x=3.2

∴The part of mixture to be drawn off and replaced with water is 3.2

Step-by-step explanation:

thanks..