(Q21).A fraction becomes equal to
4
5
 if 1 is added to both numerator and denominator. If, however, 5 is subtracted from both numerator and denominator, the fraction becomes equal to
1
2
 . What is the fraction?

Let the numerator of the fraction = x

and the denominator of the fraction = y

By problem,

x+
y+
 =
and
x-
y-
 =

⇒ (x + 1) = (y + 1) and (x – 5) = (y – 5)

x + = y + and x – = y –

⇒ x – y = – and x – y = – +

⇒ x – y = – …… (1)

and x – y = …… (2)

equation (1) × ⇒ x - y = -
equation (2) × ⇒ x - y =
-y = -
∴ y =
-
-
 =

Substituting y = in equation (2) we get

2x – = 5

⇒ 2x = 5 +

⇒ 2x = and

x =
2
 =
Thus the fraction is
x
y
 =