If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

Question

Philoid · Accepted Answer

Let the numerator be ‘a’ and denominator be ‘b’.

Given, if 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3

⇒ (a + 2)/b = 1/2

⇒ 2a + 4 = b ------ (1)

Also, a/(b – 1) = 1/3

⇒ 3a + 1 = b ------- (2)

Subtracting eq2 from eq1

⇒ 2a + 4 – 3a – 1 = b – b

⇒ a = 3

Thus, b = 2a + 4 = 10

Fraction is 3/10