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Question

Ten years ago, A was half of B in age. If the ratio of their present ages is 3 :4 then what will be the total of their present ages?

30 years

35 years

40 years

45 years

ANSWER : 2

Descrption

<pre>
Let , Ten years ago, B
was  = x 
∴ now  =  x  +  10
and Ten years ago, 
A was  = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mn>2</mn></mfrac></math>
∴ now = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mn>2</mn></mfrac></math>
<math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>  +  </mo><mn>20</mn></mrow><mn>2</mn></mfrac><mspace linebreak = "newline"/><mi>A</mi><mi>T</mi><mi>Q</mi><mo>,</mo><mo>&#xA0;</mo><mfrac><mfrac><mrow><mi>x</mi><mo>  +  </mo><mn>20</mn></mrow><mn>2</mn></mfrac><mrow><mi>x</mi><mo>  +  </mo><mn>10</mn></mrow></mfrac><mo> = </mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mfrac><mrow><mi>x</mi><mo>  +  </mo><mn>20</mn></mrow><mrow><mn>2</mn><mi>x</mi><mo>  +  </mo><mn>20</mn></mrow></mfrac><mo> = </mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mn>6</mn><mi>x</mi><mo>  +  </mo><mn>60</mn><mo> = </mo><mn>4</mn><mi>x</mi><mo>  +  </mo><mn>80</mn><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mn>6</mn><mi>x</mi><mo> - </mo><mn>4</mn><mi>x</mi><mo> = </mo><mn>80</mn><mo> - </mo><mn>60</mn><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mn>2</mn><mi>x</mi><mo> = </mo><mn>20</mn><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mi>x</mi><mo> = </mo><mfrac><mn>20</mn><mn>2</mn></mfrac><mspace linebreak = "newline"/><mo>.</mo><mo>'</mo><mo>.</mo><mi>x</mi><mo> = </mo><mn>10</mn><mspace linebreak = "newline"/><mi>P</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>&#xA0;</mo><mi>a</mi><mi>g</mi><mi>e</mi><mo>&#xA0;</mo><mi>o</mi><mi>f</mi><mo>&#xA0;</mo><mspace linebreak = "newline"/><mi>B</mi><mo>,</mo><mi>A</mi><mo>&#xA0;</mo><mo> = </mo><mi>x</mi><mo>  +  </mo><mn>10</mn><mo>&#xA0;</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo>&#xA0;</mo><mfrac><mrow><mi>x</mi><mo>  +  </mo><mn>20</mn></mrow><mn>2</mn></mfrac><mspace linebreak = "newline"/><mo> = </mo><mn>10</mn><mo>  +  </mo><mn>10</mn><mo>&#xA0;</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo>&#xA0;</mo><mfrac><mrow><mn>10</mn><mo>  +  </mo><mn>20</mn></mrow><mn>2</mn></mfrac><mspace linebreak = "newline"/><mo> = </mo><mn>20</mn><mo>&#xA0;</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo>&#xA0;</mo><mn>15</mn><mspace linebreak = "newline"/><mo>.</mo><mo>'</mo><mo>.</mo><mo>&#xA0;</mo><mi>s</mi><mi>u</mi><mi>m</mi><mo>&#xA0;</mo><mo> = </mo><mn>20</mn><mo>  +  </mo><mn>15</mn><mspace linebreak = "newline"/><mo> = </mo><mn>35</mn><mo>&#xA0;</mo><mi>y</mi><mi>e</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>&#xA0;</mo></math>
</pre>

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