The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2

Correct option is (C) 5/8

Let the original rational number is \(\frac xy.\)

According to first condition, we have

y = x + 3          ___________(1)

According to second condition, we have

\(\frac{x-3}{y+2}=\frac15\)

\(\Rightarrow\) 5x - 15 = y + 2      (By cross multiplication)

\(\Rightarrow\) 5x - 15 = (x + 3) + 2   (From (1))

\(\Rightarrow\) 5x - x = 15 + 5

\(\Rightarrow\) 4x = 20

\(\Rightarrow\) x = \(\frac{20}4\) = 5

\(\therefore\) y = 5+3 = 8            (From (1))

\(\therefore\) Original number \(=\frac xy=\frac58.\)

Correct option is C) 5/8