Question

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

Answer 1

Answer :

⟶ Original fraction = 9 / 20

Explanation :

According to the condition :

Let numerator be ' n ' and denominator be ' d '

According to the question :

• Denominator ( d ) = ( 11 + n )
• Numerator ( n ) = 8 is added = ( n + 8 )
• Denominator ( d ) = ( 11 + n ) + 8
• Answer = 3 / 4 { given }

⟶ N / D = N / D

Equation :

⟹ n + 8 / ( 11 + n ) + 8 = 3 / 4

↪cross multiply ✖

⟹ 4 ( n + 8 ) = 3 ( 11 + n ) + 8

⟹ 4n + 32 = ( 33 + 3n ) + 8

⟹ 4n - 3n = ( 33 - 32 ) + 8

⟹ 1n = 1 + 8

⟹ n = 9

To find :

➳ Numerator ( n ) = 9

➳ Denominator ( d ) = ( 11 + n ) = 11 + 9 = 20

➳ The original fraction = 9 / 20

So, It's Done !!

Answer 2

${ \bf{ \underline{ \red{ \underline{Question:-}}}}}$

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

${ \bf{ \underline{ \red{ \underline{Solution:-}}}}}$

Let, x be the numerator & y be the denominator.

• Numerator = x

• Denominator = y

{ According to question}

• Denominator = y = x + 11 ......( 1 )

8 is added to both numerator and denominator .

• Numerator = x + 8 ...... ( 2 )

• Denominator = ( x + 11 ) + 8 ....( 3 )

Fraction of Numerator & Denominator becomes 3/4 ..{ From ( 2 ) & ( 3 ) }

${ \sf{ \purple{ \dashrightarrow { \green{ \frac{ x \: + \: 8 }{( \: x \: + \: 11 \: ) \: + \: 8} = \frac{3}{4} }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ {4 ( \: x \: + \: 8 \: ) } = {3[( \: x \: + \: 11 \: ) \: + \: 8} ] }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ { 4x \: + \: 32 } = {3[ \: x \: + \: 11 \: \: + \: 8} ] }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ { 4x \: + \: 32 } = {3[ \: x \: + \: 19 \: } ] }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ { 4x \: + \: 32 } = {3x \: + \: 57 \: } }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ { 4x \: - \: 3x } = { \: 57 \: - 32 } }}}}}$

${ \sf{ \purple{ \dashrightarrow { \green{ { x } = { 25 \: } }}}}}$

Put value of x in equation ( 1 )

• Denominator = y = x + 11

• Denominator = y = 25 + 11

• Denominator = y = 36

Hence fraction of Numerator & Denominator is 25/36

i hope it helps you.