Q1 of 54 Page 77

A fraction becomes 1/3 if two is added to both numerator and denominator. If three is added to both numerator and denominator it becomes 2/5. Find the fraction.

Let numerator be x and denominator be y.


When two is added to both numerator and denominator, the


fraction becomes .



3 (x + 2) = 1(y + 2)


3x + 6 = y + 2


3x – y = 2 – 6


3x – y = – 4 ……(1)


Now if 3 is added to both numerator and denominator fraction


becomes .



5 (x + 3) = 2 (y + 3)


5x + 15 = 2y + 6


5x – 2y = 6 – 15


5x – 2y = – 9 ……(2)


Eliminate equation (1) and (2)


(3x – y = – 4) × 2


(5x – 2y = – 9) × 1



x = 1


From equation (1) we have




(∵ x = 1)


3 × 3 = y + 2


9 = y + 2


y = 7


∴ Numerator x = 1


Denominator y = 7


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