Q9 of 71 Page 68

A fraction becomes when 2 is subtracted from the numerator and denominator it becomes when 5 is added to its denominator and numerator, find the fraction.

Let the required fraction be


According to the question,



⇒ 5x – 10 = 2y – 4


⇒ 5x – 2y = 6 …(i)


Also,


⇒ 4x + 20 = 3y + 15


⇒ 4x – 3y = – 5 …(ii)


Multiply (i) by 3 and (ii) by 2,


15x – 6y = 18 ..(iii)


8x – 6y = – 10 ….(iv)


Subtract (iv) from (iii),


15x – 6y – 8x + 6y = 18 + 10


⇒ 7x = 28


⇒ x = 4


Putting this in (i),


5× 4 – 2y = 6


⇒ – 2y = 6 – 20


⇒ – 2y = – 14


⇒ y = 7


Hence the required fraction is


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