Question

23. The denominator of a fraction is greater than its numerator by 11. If 8 is
added to both its numerator and denominator, it becomes 3/4. Find
the fraction.​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The denominator of a fraction is greater than it's numerator by 11. If 8 is added to both it's numerator and denominator, it becomes 3/4.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The fraction.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the numerator be r

Let the denominator be m

$\bf{\boxed{\bf{The\:fraction\:=\frac{r}{m} }}}}}$

A/q

$\mapsto\sf{m=11+r.......................(1)}$

&

$\longrightarrow\sf{\dfrac{r+8}{m+8} =\dfrac{3}{4} }\\\\\\\longrightarrow\sf{4(r+8)=3(m+8)}\\\\\\\longrightarrow\sf{4r+32=3m+24}\\\\\\\longrightarrow\sf{4r+32=3(11+r)+24\:\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{4r+32=33+3r+24}\\\\\\\longrightarrow\sf{4r+32=3r+57}\\\\\\\longrightarrow\sf{4r-3r=57=32}\\\\\\\longrightarrow\sf{\pink{r=25}}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=11+25}\\\\\longrightarrow\sf{\pink{m=36}}$

Thus;

$\underbrace{\sf{The\:fraction\:is\:\frac{r}{m} =\frac{25}{36} }}}}$

Answer 2

$\large{\underline{\red{\rm{Question:}}}}$

The denominator of a fraction is greater than its numerator by 11. If 8 is added to

both its numerator and denominator, it becomes 3/4.Find the fraction?

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\: numerator\:of\: fraction\:be\:N}$
• $\rm{The\: denominator\:of\: fraction\:be\:D}$
• $\sf{The\: fraction be\:\dfrac{N}{D}}$

$\large{\underline{\red{\rm{To\: Find:}}}}$

• $\sf\green{The\: fraction=?}$

$\small{\underline{\purple{\rm{As\:per\:the\:1st\:case:}}}}$

$\rm{The\: D\:of\: fraction\:is\: greater\:than\: it's\:N\:by\:11}$

$\rm{\implies D=N+11}$

$\rm\green{\implies N-D=-11-----(i)}$

$\small{\underline{\purple{\rm{As\:per\:the\:2nd\:case:}}}}$

$\rm{If\: 8\:is\:added\:to\:boths\:it's\:N\:and\:D\:it\: become\:3/4}$

$\rm{\implies \dfrac{N+8}{D+8}=\dfrac{3}{4}}$

$\rm{\implies 4(N+8)=3(D+8)}$

$\rm{\implies 4N+32=3D+24}$

$\rm{\implies 4N-3D=24-32}$

$\rm\green{\implies 4N-3D=-8-----(ii)}$

• $\rm{multiplying\:by\:4\:in\:eq\:1}$

$\rm{\implies 4N-4D=-44}$

$\rm{\implies 4N-3D=-8}$

$\rm{\implies -D=-36}$

$\rm\red{\implies D=36}$

• $\sf{putting\: the\: value\:of\:D=36\:in\:eq\:1}$

$\rm{\implies N-D=-11}$

$\rm{\implies N-36=-11}$

$\rm{\implies N=-11+36}$

$\rm\red{\implies N=25}$

Hence,

$\small{\boxed{\green{\rm{The\: Fraction=\dfrac{25}{36}}}}}$