Question

A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and denominator it becomes 5/6 . Find the fraction.

Answer 1

Answer:

Explanation:

Given :-

Fraction becomes 9/11 if 2 is added to both numerator and denominator.

If 3 is added to both numerator and denominator it becomes 5/6.

Solution :-

Let the Numerator be x                  

Let the Denominator be y                  

Fraction = x/y                  

According to the Question,          

⇒ (x + 2)/y + 2 = 9/11                  

On Cross multiplying,                  

⇒ 11x + 22 = 9y + 18                  

Subtracting 22 from both sides,                  

⇒ 11x = 9y – 4                  

Dividing by 11, we get                  

⇒ x = 9y – 4/11 … (i)                  

Then,              

⇒ (x+3)/y +3 = 5/6 … (ii)                 

On Cross multiplying,                  

⇒ 6x + 18 = 5y + 15                  

Subtracting the value of x, we get                  

⇒ 6(9y – 4 )/11 + 18 = 5y + 15                  

Substituting 18 from both the sides                  

⇒ 6(9y – 4 )/11 = 5y – 3                  

⇒ 54y – 24 = 55y – 33                  

⇒ –y = – 9                  

⇒ y = 9                 

Putting this value of y in equation (i), we get                  

⇒ x = 9y – 4/11                  

⇒ x = (81 – 4)/11                  

⇒ x = 77/11                  

⇒ x = 7                 

Hence, the  fraction is 7/9.

Answer 2

$\huge \bf \underline{Answer \: }$

$\bf{ \boxed{ \blue{ \tt{ \frac{7}{9 \: }}}}}$

______________________________

$\bf \huge \underline{Question}$

A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and denominator it becomes 5/6 . Find the fraction.

_________________________________

$\bf \underline{step \: by \: step \: explanation}$

$\sf{let \: numerator \: be \: x}$

$\sf{denominator \: be \: y}$

$\sf{fraction \: is \: \frac{x}{y}}$

________________________________

From the question

$\rm{⇒ \frac{(x + 2)}{y} + 2 = \frac{9}{11}}$

Now we have to multipy the cross

$\rm{⇒11x + 22 = 9y + 18}$

$\rm{⇒11x = 9y - 4}$

Now dividing by 11 we get,

$\rm{⇒x = 9y - \frac{4}{11} is \: (eq1)}$

$\rm{⇒ \frac{(x + 3)}{(y + 3)} = \frac{5}{6} is \: (eq2)}$

Now again cross multiplying

$\rm{⇒6x + 18 = 5y + 15}$

Now subtracting the value of x so we get,

$\rm{⇒ \frac{6(9y - 4)}{11 + 18} = 5y + 15}$

we have to add both sides subtracting 4 from this solution we get,

$\rm{⇒ \frac{6(9y - 4)}{11} = 5y - 3}$

$\rm{⇒54 - 24 = 55y - 33}$

then

$\rm{⇒ - y = - 9}$

$\rm{answer \: is \: y = 9}$

__________________________

Now putting the value of y in eq 1 we get,

$\tt{⇒x = 9y - 4}$

$\rm{⇒x = \frac{(9 \times 9 - 4)}{11}}$

$\tt{⇒x = \frac{(81 - 4)}{77}}$

$\tt{⇒x = \frac{77}{11}}$

$\tt{⇒x = 7}$

so,

$\bf{ \boxed{ \green{ \tt{answer \: is \: fraction = \frac{7}{9 \: }}}}}$

I hope it's help uh