Question

The denominator of a fraction is 4 more than the numerator.If one is added to both numerator and denominator then the fraction becomes 12. Find the fraction.

Answer 1

Correct Question :-

The denominator of a fraction is 4 more than the numerator. If one is added to both numerator and denominator then the fraction becomes 1/2 . Find the fraction.

Answer :- 3/7

Solution :-

Let the numerator and denominator be x and y respectively.

According to the question:

• Case 1

Denominator is 4 more than the numerator.

⇒ x - y = -4 ...(1)

• Case 2

If 1 is added to both the numerator and denominator then the fraction becomes 12.

⇒ (x + 1) / (y + 1) = 1/2

⇒ 2x + 2 = y + 1

⇒ 2x - y = -1 ...(2)

Subtracting (1) from (2), we get

⇒ 2x - y - x + y = -1 - (-4)

⇒ x = 4 - 1

⇒ x = 3

Substituting [x = 3] in (1)

⇒ 3 - y = -4

⇒ -y = -7

⇒ y = 7

Here, x = 3 and y = 7,

∴ Fraction = 3/7

Why the question you posted is a bit incorrect by mistake?

If you assume the case 2 ( If one is added to both numerator and denominator then the fraction becomes 12 ) then the Linear equation for this would be x - 12y = 11 [ which means x is greater than 12 times of y , but this contradicts the fact that denominator is 4 more than the numerator ({see (1) }

Answer 2

.°. Fraction = 3/7 .

Given :

1. The denominator of a fraction is 4 more than the numerator .
2. If one is added to both numerator and denominator then the fraction becomes ½.

To Find :-

• The fraction.

Solution :-

Let, the denominator of a fraction be "r" and numerator of a fraction be "s".

• According to first statement .

=> r - s = -4 ----------(I)

• According to second statement.

=> (r + 1) / (s + 1 ) = 1/2

=> 2(r + 1) = s + 1

=> 2r + 2 = s + 1

=> 2r - s = -1 ---------(II)

Subtracting (I) & (II),

=> 2r - s - r - s = -1 - (-4)

=> r = 4 - 1

=> r = 3 .

Put r =3 in eqn. (I)

=> 3 - s = -4

=> -s = -4 - 3

=> -s = -7

=> s = 7 .

.°. The fraction is 3/7.