Q) A fraction becomes 
when 1 is subtracted from the numerator. It becomes 
when 8 is added to the denominator. Find the fraction.
Ans: Let’s consider the fraction is 
First, when 1 is subtracted from numerator, then:
=
∴ 3 (P -1) = Q
∴ 3P – Q = 3 …………… (i)
Next, when 8 is added to the denominator, then:
=
∴ 4 P = Q + 8
∴ 4 P – Q = 8 ………….. (ii)
By solving equation (i) and equation (ii), we get:
P = 5
and Q = 12
Therefore, the fraction is 
.