Question

the number of a fraction is 6 less than a denominator. if 1 is added to both the denominator the fraction becomes 1/2 . find the fraction​

Answer 1

GIVEN:

• The numerator of a fraction is 6 less than a denominator.
• if 1 is added to both the denominator the fraction becomes 1/2 .

TO FIND:

• What is the fraction ?

SOLUTION:

Let the fraction be x/y

• NUMERATOR = x
• DENOMINATOR = y
• FRACTION = x/y

CASE:- 1)

• The numerator of a fraction is 6 less than a denominator.

According to question:-

$\bf{\longmapsto x = y -6....1)}$

CASE:- 2)

• if 1 is added to both numerator and denominator the fraction becomes 1/2.

According to question:-

$\sf{\longmapsto \dfrac{x+1}{y+1} = \dfrac{1}{2} }$

$\sf{\longmapsto 2(x+1) = y+1 }$

$\sf{\longmapsto 2x + 2 = y+1 }$

$\sf{\longmapsto 2x -y = 1-2 }$

$\bf{\longmapsto 2x -y = -1....2)}$

Put the value of 'x' from equation 1)

$\sf{\longmapsto 2(y-6) -y = -1}$

$\sf{\longmapsto 2y -12 -y = -1}$

$\sf{\longmapsto y = -1+12}$

$\bf{\longmapsto y = 11 }$

Put the value of 'y' in equation 1)

$\sf{\longmapsto x = 11-6 }$

$\bf{\longmapsto x = 5 }$

• NUMERATOR = x = 5
• DENOMINATOR = y = 11

$\large{\boxed{\bf{\star \: FRACTION = \dfrac{x}{y} = \dfrac{5}{11} \: \star}}}$

❝ Hence, the fraction formed is 5/11 ❞

______________________

Answer 2

Answer:

$\huge\bold\star\red{Answer}\star$

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Given:-

• the numerator of a fraction is 6 less than the denominator.
• If 1 added to both numerator and denominator the fraction becomes $\frac{1}{2}$

To find:-

• The fraction

Solution:-

Let,the numerator be x and the denominator be y

•°•the fraction will be $\frac{x}{y}$

According to the Q,

x=y-6........(i)

again,

$\mathsf{ \dfrac{x+1}{y+1}}$=$\mathsf{ \dfrac{1}{2}}$

$\implies$2x+2=y+1

$\implies$2x-y=(-1)..............(ii)

putting the value of x in eq (ii)

$\: \: \: \: 2(y-6)-y=(-1)$

$\implies$ 2y-12-y=(-1)

$\implies$ y=(-1)+12

$\implies$ y=11

•°•the fraction will be $\frac{5}{11}$

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$\huge\green{Thanks}$