Question

14. A fraction is such that the numerator is 2 less than the denominator. If 3 is added to the numerator and 5 to the denominator, the fraction becomes 3 upon 5 .find the fraction.​

Answer 1

Given :

• Numerator is 2 less than the Denominator .
• If 3 is added to the Numerator and 5 to the denominator,the fraction becomes 3/5 .

To Find :

• Find the Original Fraction

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

SolutioN : By forming the Equation we can Calculate the Value of y . We can Calculate the fraction . Let's Solve :

$\dag$ Calculating the Value of y :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \bigg\{ \dfrac{Numerator}{Denominator} \bigg\} = \bigg\{ \dfrac{y}{y + 2} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \bigg\{ \dfrac{y + 3}{y + (2 + 5)} \bigg\} = \bigg\{ \dfrac{3}{5} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \bigg\{ \dfrac{y + 3}{y + 7} \bigg\} = \bigg\{ \dfrac{3}{5} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 5 \bigg( y + 3 \bigg) = 3 \bigg( y + 7 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 5y + 15 = 3y + 21 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 5y - 3y = 21 - 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 5y - 3y = 6 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 2y = 6 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { y = \dfrac{6}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { y = \cancel\dfrac{6}{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\purple{\frak { y = 3 }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Fraction :

• Numerator = y = 3
• Denominator = y + 2 = 3 + 2 = 5

$\therefore \;$ Original Fraction is ⅗ .

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Answer 2

$\underline{\underline{\pink{\huge\sf Solution}}}$

Let the original denominator be x

✴️To find :-

(x-2)/x.

✴️Solving :-

{(x-2) +3} /{x+5}= 3/5

Or,

{x+1} /{x+5} = 3/5

Or,

5x+5= 3x+15

Or,

2x= 10

Therefore, x= 5

✴️Required fraction :-

= (x-2) / x= 3/5.

✴️Verification :-

(3+3)/(5+5)= 6/10 = 3/5.

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Hope it helped ya ✌️