Q26 of 186 Page 4

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, then are in the ratio 2 : 3. Determine the fraction.

Let the numerator = x

and the denominator = y


So, the fraction


According to the question,


Condition I:


x + y = 2x + 4


⇒ x + y – 2x = 4


⇒ – x + y = 4


⇒ y = 4 + x …(i)


Condition II:



⇒ 3(x + 3) = 2( y + 3)


⇒ 3x + 9 = 2y + 6


⇒ 3x – 2y = – 3 …(ii)


On putting the value of y in Eq.(ii) , we get


3x – 2(4 + x) = – 3


⇒ 3x – 8 – 2x = – 3


⇒ x = 5


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


y = 4 + 5


⇒ y = 9


So, the numerator is 5 and the denominator is 9


Hence, the fraction is


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