When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.
Let the numerator be ‘a’ and denominator be ‘b’
Given, 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4.
⇒ 4a – 8 = b + 3
⇒ 4a – b = 11 ------ (1)
Also, when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3.
⇒ 3a + 18 = 2b
⇒ a + 6 = 2b -------- (2)
Multiplying eq2 by 4 and subtracting from eq1
⇒ 4a – b – 4a – 24 = 11 – 8b
⇒ 7b = 35
⇒ b = 5
Thus, a = 4
Fraction is 4/5