Q27 of 186 Page 4

The sum of the numerator and denominator of a fraction is 8. If 3 is added to both 3 the numerator and the denominator, the fraction becomes 3/4. Find the fraction.

Let the numerator = x

and the denominator = y


So, the fraction


According to the question,


Condition I:


x + y = 8


⇒ y = 8 – x …(i)


Condition II:



⇒ 4(x + 3) = 3( y + 3)


⇒ 4x + 12 = 3y + 9


⇒ 4x – 3y = – 3 …(ii)


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


4x – 3(8 – x) = – 3


⇒ 4x – 24 + 3x = – 3


⇒ 7x = 21


⇒ x = 3


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


y = 8 – 3


⇒ y = 5


So, the numerator is 3 and the denominator is 5


Hence, the fraction is


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