Question
A fraction becomes 1/6 when 4 is subtracted from its
numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes 1/3. Then, the LCM of the numerator and denominator of the said fraction, must beSolution
Let the original fraction be x/y ⇒ (x - 4)/(y + 1) = 1/6 ⇒ 6x – 24 = y + 1 ⇒ 6x - y = 25……….(i) Again, ⇒ (x + 2)/(y + 1) = 1/3 ⇒ 3x + 6 = y + 1 ⇒ 3x - y = -5………(ii) By solving equation (i) and (ii) We get x = 10 and y = 35 So LCM of 10 and 35 = 70
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