**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 .**