Question

The denominator of a rational number is less than its numerator than 5. If the 5 is added to the numerator, the new number becomes 11 by 6.Find the original number. ​

Answer 1

Question:-

• The denominator of a rational number is less than its numerator than 5. If the 5 is added to the numerator, the new number becomes 11 by 6.Find the original number.

To Find:-

• Find the number.

Solution:-

• Let the numerator be x

• Denominator be x - 5

According to the Question:-

$\sf\longrightarrow \: \dfrac { x + 5 } { x - 5 } = \dfrac { 11 } { 6 }$

$\sf\longrightarrow \: 6( x + 5 ) = 11( x - 5 )$

$\sf\longrightarrow \: 6x + 30 = 11x - 55$

$\sf\longrightarrow \: 11x - 6x = 55 + 30$

$\sf\longrightarrow \: 5x = 85$

$\sf\longrightarrow \: x = \cancel\dfrac { 85 } { 5 }$

$\sf\longrightarrow \: x = 17$

Hence ,

• Numerator is x = 17

• Denominator is x - 5 = 12

Answer 2

$Question:-</p><p></p><p>The denominator of a rational number is less than its numerator than 5. If the 5 is added to the numerator, the new number becomes 11 by 6.Find the original number.</p><p></p><p>To Find:-</p><p></p><p>Find the number.</p><p></p><p>Solution:-</p><p></p><p>Let the numerator be x</p><p></p><p>Denominator be x - 5</p><p></p><p>According to the Question:-</p><p></p><p>\sf\longrightarrow \: \dfrac { x + 5 } { x - 5 } = \dfrac { 11 } { 6 }⟶x−5x+5=611</p><p></p><p>\sf\longrightarrow \: 6( x + 5 ) = 11( x - 5 )⟶6(x+5)=11(x−5)</p><p></p><p>\sf\longrightarrow \: 6x + 30 = 11x - 55⟶6x+30=11x−55</p><p></p><p>\sf\longrightarrow \: 11x - 6x = 55 + 30⟶11x−6x=55+30</p><p></p><p>\sf\longrightarrow \: 5x = 85⟶5x=85</p><p></p><p>\sf\longrightarrow \: x = \cancel\dfrac { 85 } { 5 }⟶x=585</p><p></p><p>\sf\longrightarrow \: x = 17⟶x=17</p><p></p><p>Hence ,</p><p></p><p>Numerator is x = 17</p><p></p><p>Denominator is x - 5 = 12</p><p></p><p>$