Q13 of 186 Page 4

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Let the numerator = x

and the denominator = y


So, the fraction


According to the question,


Condition I:



⇒ 3(x – 1) = y


⇒ 3x – 3 = y


⇒ 3x – y – 3 = 0 …(i)


Condition II:



⇒ 4x = y + 8


⇒ 4x – y = 8


⇒ 4x – y – 8 = 0 …(ii)


By cross - multiplication method, we have





On taking I and III ratio, we get



⇒ x = 5


On taking II and III ratio, we get



⇒ y = 12


So, the numerator is 5 and the denominator is 12


Hence, the fraction is


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