Question

The numerator of a fraction is 4 less than denominator. If 1 is added to both its numerator and denominator, it becomes 1/2.Find the fraction ?​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• The fraction is 3/7.

Given That:

• The numerator of a fraction is 4 less than the denominator.
• 1 is added to both its numerator and denominator, it becomes 1/2.

Need To Find:

• The Fraction = ?

ExPlanation:

Let the fraction to be predicted a/b.

According to the given condition:

Numerator = denominator -4

➠ a = b - 4

➠ b - a = 4

As per the given data:

if 1 added to both numerator and denominator then fraction becomes 1/2.

➠ a + 1/b + 1 = 1/2

On cross multiplying the above equation we get,

➠2a + 2 = b + 1

➠2a - b = -1

➠(2a - b) + (b - a)

➠ 4 - 1

• a = 3 and b = 7

ThereFore:

• The Fraction = 3/7.

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Answer 2

Given :

• The numerator of a fraction is 4 less than denominator.
• If 1 is added to both its numerator and denominator, it becomes 1/2.

To find :

• The fraction.

Solution :

Let the numerator of the fraction be x and the denominator be y .

According to 1st condition :-

• The numerator of a fraction is 4 less than denominator.

$\implies\sf{x=y-4...........eq(1)}$

According to 2nd condition :-

• If 1 is added to both its numerator and denominator, it becomes 1/2.

$\implies\sf{\frac{x+1}{y+1}=\frac{1}{2}}$

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

Put x= y-4 from eq(1).

$\implies\sf{2(y-4)+2=y+1}$

$\implies\sf{2y-8+2=y+1}$

$\implies\sf{2y-y=1-2+8}$

$\implies\sf{y=7}$

${\boxed{\bold{y=7}}}$

Now put y = 7 in eq (1) for getting the value of x.

$\implies\sf{x=y-4}$

$\implies\sf{x=7-4}$

$\implies\sf{x=3}$

${\boxed{\bold{x=3}}}$

• Numerator = 3
• Denominator = 7

We know,

${\boxed{\bold{Fraction=\dfrac{Numerator}{Denominator}}}}$

Therefore,

$\sf{Fraction=\dfrac{x}{y}=\dfrac{3}{7}}$