Question

The denominator of a fraction is 4 more than twice the numerator. When both numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Find the fraction.​

Answer 1

Answer:

Let the numerator be x and the denominator be y.

y = 4 + 2x

2x - y = -4 ...(i)

When both numerator and denominator are decreased by 6, then,

the numerator is (x - 6) and the denominator is (y - 6).

Now,

y - 6 = 12(x - 6)

y - 6 = 12x - 72

12x - y = 72 - 6

12x - y = 66 ...(ii)

Solving (i) and (ii),

2x - y = -4

12x - y = 66

-10x = -70

→ x = 70/10 = 7

→ y = 18

→ x/y = 7/18

Therefore, the fraction x/y is 7/18.

Answer 2

Step-by-step explanation:

Solution :

Let,

• Numerator = x
• Denominator = y

Fraction = x/y

The denominator of a fraction is 4 more than twice the numerator.

⇒ y = 2x + 4

2x - y + 4 = 0 ----------- (i)

When both numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator.

⇒ (y - 6) = 12 (x - 6)

⇒ y - 6 = 12x - 72

12x - y - 66 = 0 ---------- (ii)

Subatract eq. (i) from eq. (ii)

⇒ 10x - 70 = 0

⇒ x = 7

Substitute value of x in eq. (i)

⇒ 2x - y + 4 = 0

⇒ 14 - y + 4 = 0

⇒ y = 18

Fraction = 7/18

Therefore, the fraction is 7/18