The numerator of a fraction is 2 less than its denominator. If the numeratoris multiplied by 2 and the denominator is multiplied by 3, then the fractionbecomes 2/9. The fraction is,

Correct option is A

Let the fraction be x/y, where the numerator x is 2 less than the denominator y.

So, we write the equation:
x = y - 2

According to the problem, when the numerator is multiplied by 2 and the denominator by 3, the fraction becomes 2/9.
​$$\frac{2x}{3y} = \frac{2}{9}$$​​

• Cross multiply:$$2x \times 9 = 2 \times 3y$$

  $$18x = 6y$$

  $$3x = y$$​​​​

• Substituting x = y - 2 into 3x = y:$$3(y - 2) = y$$

  $$3y - 6 = y$$

  $$3y - y = 6$$

  $$2y = 6$$

  $$y = 3$$​​​​​​

  Finding x: x = y - 2 = 3 - 2 = 1

So, the fraction is 1/3, which matches option (A) 1/3.