Question

(m) The denominator of a fraction is 4 more than twice its numerator. Denominator
becomes 12 times the numerator, if both the numentor and the denominator
are reduced by 6. Find the fraction​

Answer 1

✬ Fraction = 7/18 ✬

Step-by-step explanation:

Given:

• Denominator of a fraction is 4 more than twice its numerator.
• If both the numerator & denominator is reduced by 6 then denominator becomes 12 times the numerator.

To Find:

• What is the fraction ?

Solution: Let the numerator be x and denominator be y. Therefore,

➼ y = 4 more than 2 times of x

➼ y = (4 + 2x)

• Fraction = x/y

A/q

• Denominator becomes 12 times the numerator after subtracting 6 from both x and y.

➟ 12(x – 6) = (y – 6)

➟ 12x – 72 = 4 + 2x – 6

➟ 12x – 2x = 4 – 6 + 72

➟ 10x = –2 + 72

➟ 10x = 70

➟ x = 70/10

➟ x = 7

So the numerator is 7 , Now put to value of x in eqⁿ ( i ) to get the value of y.

➼ y = (4 + 2x)

➼ y = 4 + 2 × 7

➼ y = 4 + 14

➼ y = 18

So the denominator is 18 & hence the required fraction is x/y = 7/18

Answer 2

Answer:

Given :-

• The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 twice the numerator, if both the numerator and the denominator are reduced by 6.

To Find :-

• What is the fraction.

Solution :-

Let, the numerator be x

And, the denominator will be 2x + 4

Then, the fraction will be $\sf \dfrac{x}{2x + 4}$

According to the question,

⇒ $\sf \dfrac{x - 6}{2x + 4 - 6} =\: \dfrac{1}{12}$

By doing cross multiplication we get,

⇒ $\sf 12(x - 6) =\: 2x + 4 - 6$

⇒ $\sf 12x - 72 = 2x - 2$

⇒ $\sf 12x - 2x =\: - 2 + 72$

⇒ $\sf 10x = 70$

⇒ $\sf x =\: \dfrac{\cancel{70}}{\cancel{10}}$

➠ $\sf\bold{\green{x =\: 7}}$

Hence, the required fraction will be,

↦ $\sf \dfrac{x}{2x + 4}$

↦ $\sf \dfrac{7}{7(2) + 4}$

↦ $\sf \dfrac{7}{14 + 4}$

➦ $\sf\bold{\purple{\dfrac{7}{18}}}$

$\therefore$ The required fraction is ${\red{\boxed{\large{\bold{\dfrac{7}{18}}}}}}$

VERIFICATION :-

↦ $\sf \dfrac{x - 6}{2x + 4 - 6} =\: \dfrac{1}{12}$

By putting x = 7 we get,

↦ $\sf \dfrac{7 - 6}{2(7) + 4 - 6} =\: \dfrac{1}{12}$

↦ $\sf \dfrac{1}{14 + 4 - 6} =\: \dfrac{1}{12}$

↦ $\sf\bold{\pink{\dfrac{1}{12} =\: \dfrac{1}{12}}}$

➦ LHS = RHS

Hence, Verified ✔