A container is filled with a mixture containing 40% water and the rest milk. A certain portion of this mixture is removed and replaced with another mi...

Question

A container is filled with a mixture containing 40% water and the rest milk. A certain portion of this mixture is removed and replaced with another mixture that contains 81% milk and the remaining water. After this replacement, the new mixture has 74% milk. What fraction of the original mixture was replaced?

Options

A.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotationencoding="application/xtex">13</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.1901em;verticalalign:0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">3</span></span></span></span><spanstyle="top:3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="fracline"style="borderbottomwidth:0.04em;"></span></span><spanstyle="top:3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">1</span></span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>

B.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotationencoding="application/xtex">23</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.1901em;verticalalign:0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">3</span></span></span></span><spanstyle="top:3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="fracline"style="borderbottomwidth:0.04em;"></span></span><spanstyle="top:3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">2</span></span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2}{3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>

C.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac></mrow><annotationencoding="application/xtex">25</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.1901em;verticalalign:0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">5</span></span></span></span><spanstyle="top:3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="fracline"style="borderbottomwidth:0.04em;"></span></span><spanstyle="top:3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">2</span></span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2}{5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>

D.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>3</mn><mn>5</mn></mfrac></mrow><annotationencoding="application/xtex">35</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.1901em;verticalalign:0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">5</span></span></span></span><spanstyle="top:3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="fracline"style="borderbottomwidth:0.04em;"></span></span><spanstyle="top:3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">3</span></span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>3</mn><mn>5</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{3}{5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>

E.

None of These

mixturepercentagereplacementmilk and water

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