Question

Sum of Numerator and denominator of a fraction is 15, if numerator is 5 less than denominator then numerator is ______​

Answer 1

Given : Sum of numerator and denominator is 15 , Numerator is 5 less than the Denominator .

To Find : Find the Numerator

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN : For Solving this question let's form the Equation first .Than, we can Solve it .Let's Solve :

$\maltese$ According to the Question :

$\longmapsto$ Let the Denominator be y .So,

$\qquad \; {\sf{\pmb{ Denominator = y }}}$

$\longmapsto$ Numerator is 5 less than the Denominator .So,

$\qquad \; {\pmb{\sf{ Numerator = y - 5 }}}$

$\longmapsto$ Sum of these Numbers is 15 .So,

$\qquad \; {\sf{ y + \bigg( y - 5 \bigg) = 15 }}$

$\maltese$ Calculating the Value of y :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { y + \bigg( y - 5 \bigg) = 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 2y - 5 = 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 2y = 15 + 5 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 2y = 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { y = \dfrac{20}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { y = \cancel\dfrac{20}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak{ y = 10 }}}}} \; {\pink{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Fraction :

• Denominator = y = 10
• Numerator = y - 5 = 10 - 5 = 5

$\therefore \;$ Numerator of the fraction is 5 .

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Answer 2

Given,

Sum of Numerator and Denominator of a fraction is 15.

Numerator is 5 lessthan Denominator.

find the numerator

Solution :-

let us assume,

Denominator = y

Numerator = y - 5

according to the question,

$\rm⇢ \: \: y + (y - 5) = 15$

$\rm⇢ \: \: 2y = 15 + 5$

$\rm⇢ \: \: y = 10$

then, Denominator = 10

and, Numerator = y - 5 = 5

FINAL ANSWER :-

Numerator is 5