Question

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

Answer 1

Answer:

7/18

Step-by-step explanation:

Let the numerator be 'x' and denominator be 'y'. Thus, fraction be x/y.

 y = 4 + 2x      {given}

Denominator  becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6.  Means,

If denominator = y - 6  &

  numerator = x - 6

⇒ denominator = 12 times of numerator

⇒ (y - 6) = 12(x - 6)

⇒ (4 + 2x - 6) = 12x - 72

⇒ 72 + 4 - 6 = 12x - 2x

⇒ 70 = 10x          ⇒ x = 7

  Thus, y = 4 + 2x = 4 + 2(7)=18

∴ Fraction = x/y = 7/18

Answer 2

Question:-

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

To Find:-

• Find the fraction.

Solution:-

• Let the numerator be ' x '

• Denominator be ' y '

According to the Question:-

Given ,

• y = 2x + 4

$\longrightarrow\sf \: y - 6 = 12( x - 6 )$

$\longrightarrow\sf \: 2x + 4 - 6 = 12x - 72$

$\longrightarrow\sf \: 2x - 2 = 12x - 72$

$\longrightarrow\sf \: 12x - 2x = 72 - 2$

$\longrightarrow\sf \: 10x = 70$

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

$\longrightarrow\sf \: x = 7$

Hence ,

• Numerator is 7

• Denominator is 2x + 4 = 18