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

Let the fraction be `x/"y"` .

Denominator of a fraction is 4 more than twice its numerator.

So, `"y" = 4 + 2x`

⇒ `2x - "y" = – 4`  ......(I)

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

So, `"y" - 6 = 12(x - 6)`

⇒ `"y" - 6 = 12x - 72`

⇒ `12x - "y" = 72 - 6 = 66`

⇒ `12x - "y" = 66` ......(II)

Subtracting (I) from (II)

`12x - 2x - "y" - (- "y") = 66 - (- 4)`

⇒ `10x - 70`

⇒ `x = 70/10 = 7`

⇒ `x = 7`

Putting the value of x = 7 in (I)

`2(7) - "y" = - 4`

⇒ `14 - "y" = - 4`

⇒ `"y" = 14 + 4 = 18`

Thus, the fraction obtained is `7/18`.