Question

the denominator of fraction is 9 more than its numerator if the numerator and the denominator both are increased by 7,the new fraction becomes 7/10 find the original fraction​

Answer 1

Answer:

The original fraction = 14/23

Step-by-step explanation:

Given,

• The denominator of fraction is 9 more than its numerator
• If the numerator and the denominator both are increased by 7, the new fraction becomes 7/10

To find,

• the original fraction

Solution,

 Let the numerator of the fraction be 'x'

The denominator = x + 9

   $\bf fraction=\frac{numerator}{denominator}$

The original fraction = x/(x + 9)

Now,

if the numerator and the denominator both are increased by 7,the new fraction becomes 7/10

     

         $\sf \frac{x+7}{x+9+7} =\frac{7}{10} \\\\ \frac{x+7}{x+16} =\frac{7}{10} \\\\ 10(x+7)=7(x+16) \\\\ 10x+70=7x+112 \\\\ 10x-7x=112-70 \\\\3x=42 \\\\ x=42/3 \\\\ x=14$

⇒ The value of x is 14

i.e., numerator = 14

⇒ denominator = 14 + 9 = 23

The original fraction = 14/23

Verification :

The original fraction = 14/23

Condition :

if the numerator and the denominator both are increased by 7,the new fraction becomes 7/10

   $\sf \frac{14+7}{23+7} = \frac{7}{10} \\\\ \frac{21}{30} =\frac{7}{10} \\\\ \frac{7 \times 3}{3 \times 10} = \frac{7}{10} \\\\ \frac{7}{10}= \frac{7}{10} \\\\ LHS=RHS$

Hence verified!

Answer 2

Given: The denominator of fraction is 9 more than its numerator if the numerator and the denominator both are increased by 7,The new fraction becomes 7/10

To Find: Original fraction

$\: \: \: \: \: \: \:$_____________________

Let the denominator be x and numerator is x + 9

• If 7 is added to the numerator and denominator, the fraction becomes 7/10.

✞According to Question,

$\sf : \implies \dfrac{(x + 7 )}{(x + 7 + 9} = \dfrac{7}{10} \\ \\ \\ \sf : \implies \frac{(x + 7)}{(x + 16)} = \frac{7}{10} \\ \\ \\ \sf : \implies10(x + 7) = 7(x + 16) \\ \\ \\ \sf : \implies10x + 70 = 7x + 112 \\ \\ \\ \sf \implies10x - 7x = 112 - 70 \\ \\ \\ \sf : \implies \: 3x = 42 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: { \boxed{ \bf{ x = 14}}} \: \pink{ \star}$

Hence,

• Denominator = 14

• Numerator = 14 + 9 = 23

${{ \boxed{ \bf{\therefore { \: The \: original \: fraction \: is \: \frac{14}{23} }}}}} \: \red{ \star}$

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