A fraction becomes 7/8, if 5 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 6/7. Find the fraction.

Let the fraction be x/y,
According to the question,
(x + 5) / (y + 5) = 7/8
⇒ 8x + 40 = 7x + 35
∴ 8x - 7y = -5 ..(i)
Again, according to the question,
(x + 3)/(y + 3) = 6/7
⇒ 7x + 21 = 6y + 18
∴ 7x - 6y = -3 ..(ii)
On multiplying Eq. (i) by 6 and Eq. (ii) by 7 and subtracting, we get
48x - 42y = -30
49x - 42y = -21
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-x = -9
∴ x = 9
On putting te value of x in Eq. (i) , we get
72 - 7y = -5
⇒ -7y = -5 - 72
⇒ y = -5 - 72
⇒ y = (-77) / (-7) = 11
∴ Required fraction = 9/11