The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Let the numerator be ‘a’ and denominator be ‘b’.
Given, sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.
⇒ a + b = 12 ------ (1)
Also, a/(b + 3) = 1/2
⇒ 2a – b = 3 ------- (2)
Adding eq1 and eq2
⇒ a + b + 2a – b = 15
⇒ 3a = 15
⇒ a = 5
Thus, b = 7
Fraction is 5/7.