Q25 of 186 Page 4

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Let the numerator = x

and the denominator = y


So, the fraction


According to the question,


Condition I:


x + y = 2y – 3


⇒ x + y – 2y = – 3


⇒ x – y = – 3 …(i)


Condition II:



⇒ 2(x – 1) = y – 1


⇒ 2x – 2 = y – 1


⇒ 2x – y = 1 …(ii)


On subtracting Eq. (i) from Eq. (ii), we get


2x – y – x + y = 1 + 3


⇒ x = 4


On putting the value of x in Eq. (i), we get


4 – y = – 3


⇒ y = 7


So, the numerator is 4 and the denominator is 7


Hence, the fraction is


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