Q5 of 40 Page 92

A fraction becomes equal to if 1 is added to both numerator and denominator. If however, 5 is subtracted from both numerator and denominator, the fraction becomes equal to What is the fraction?

Let the numerator be x and denominator be y.

Hence, the fraction =


Then, according to first condition, we have


and


⇒ 5x + 5 = 4y + 4


⇒ 5x – 4y = -1 ….I


According to second condition,



⇒ 2x – 10 = y – 5 …II


Using the elimination method, multiplying eq. I by 2 and Eq. II by 5


10x – 8y = -2


10x – 5y = 25


- + - _


-3y = -27


y = 9


substitute the value of y = 9 in Eq. I


5x – 4(9) + 1 = 0


5x = -1 + 36


x = 7


hence, the given fraction is .


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