#### Question

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with `1/2`. Find the fraction.

#### Solution

Let the numerator of the fraction be x.

∴ Denominator = x + 12

∴ The fraction = `"x"/("x" + 12)`

If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction obtained is `1/2`.

From the given information,

`("x" - 2)/("x" + 12 + 7) = 1/2`

⇒ 2 (x - 2) = 1 ( x + 12 +7)

⇒ 2x - 4 = x + 19

⇒ 2x - x = 19 + 4

⇒ x = 23

∴ Numerator of the fraction is 23.

∴ Denominator of the fraction is 23 + 12 = 35.

Hence, the fraction is `23/35`.

Is there an error in this question or solution?

Solution The Denominator of a Fraction is Greater than Its Numerator by 12. If the Numerator is Decreased by 2 and the Denominator is Increased by 7, Concept: Word Problems of Equation in One Variable.