Q10 of 186 Page 4

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we add 1 to the denominator. What is the fraction?

Let the numerator = x

and the denominator = y


So, the fraction


According to the question,


Condition I:



⇒ x + 1 = y – 1


⇒ x – y = – 2


⇒ x – y + 2 = 0 …(i)


Condition II:



⇒ 2x = y + 1


⇒ 2x – y = 1


⇒ 2x – y – 1 = 0 …(ii)


By cross - multiplication method, we have





On taking I and III ratio, we get



⇒ x = 3


On taking II and III ratio, we get



⇒ y = 5


So, the numerator is 3 and the denominator is 5


Hence, the fraction is


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