The ratio of boys to girls in a class 2/5. If 2 boys leave and 4 girls join the class, the ratio of the boys to the girls becomes 1/4. Originally, how many girls were in the class?
Correct Answer: 20
Let, Originally, there were 2x boys and 5x girls in the classNow, <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi><mo> - </mo><mn>2</mn></mrow><mrow><mn>5</mn><mi>x</mi><mo> + </mo><mn>4</mn></mrow></mfrac><mo> = </mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mspace linebreak = "newline"/><mo>⇒</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mi>x</mi><mo> - </mo><mn>2</mn></mrow></mfenced><mo> = </mo><mn>5</mn><mi>x</mi><mo> + </mo><mn>4</mn><mspace linebreak = "newline"/><mo>⇒</mo><mn>8</mn><mi>x</mi><mo> - </mo><mn>8</mn><mo> = </mo><mn>5</mn><mi>x</mi><mo> + </mo><mn>4</mn><mspace linebreak = "newline"/><mo>⇒</mo><mn>8</mn><mi>x</mi><mo> - </mo><mn>5</mn><mi>x</mi><mo> = </mo><mn>4</mn><mo> + </mo><mn>8</mn><mspace linebreak = "newline"/><mo>⇒</mo><mn>3</mn><mi>x</mi><mo> = </mo><mn>12</mn><mspace linebreak = "newline"/><mo>∴</mo></math> x = 4<math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Originally number of girls = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>×</mo><mn>4</mn><mo> = </mo><mn>20</mn></math>