Question

The numerator of a fraction is 4 less than the denominator. If one is added to both it's numerator and denominator, the fraction becomes 1 by 2. Find the fraction.​

Answer 1

Answer :

3/7

Solution :

Let N be the numerator and D be the denominator so that the required fraction will be N/D .

Now ,

According to the question , the numerator of a fraction is 4 less than the denominator .

Thus ,

N = D - 4 ------(1)

Also ,

If one is added to both it's numerator and denominator, the fraction becomes 1/2 .

Thus ,

=> (N + 1)/(D + 1) = 1/2

=> (D - 4 + 1)/(D + 1) = 1/2

=> (D - 3)/(D + 1) = 1/2

=> 2•(D - 3) = 1•(D + 1)

=> 2D - 6 = D + 1

=> 2D - D = 1 + 6

=> D = 7

Now ,

Putting D = 7 in eq-(1) , we get ;

=> N = D - 4

=> N = 7 - 4

=> N = 3

Hence ,

Required fraction is 3/7 .

Answer 2

$\huge{\boxed{\mathtt{\red{Correct \: , Question}}}}$

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

$\frac{1}{2}$

Find the Fraction.

$\huge\mathbb\purple{ANSWER}$

$\huge{\boxed{\mathtt{\orange{ \frac{3}{7} }}}}$

$\huge{\boxed{\boxed{\green{\ulcorner{\mid{ \overline{\underline{\bf{SoLuTiOn}}}}}\mid}}}}$

$Let \: the \: fraction \: be \: \frac{a}{b}$

Numerator= denominator -4

a = b - 4 ➡️ b - a = 4

if 1 added to both numerator and denomator then fraction

$= \frac{1}{2}$

$\frac{a + 1}{b + 1} = \frac{1}{2}$

2 a + 2 = b + 1

2 a - b = -1

(2a -b )+( b - a ) = 4 -1

a = 3,b = 7

Fraction ⭐⬇️

$\frac{3}{7}$

$\huge{\mathcal{\blue{\underline{thanks \infty }}}}$