Question

50. The numerator of a rational number is less than its denominator by 3. If the numerator becomes three times and the denominator is increased by 20, the new number becomes ⅛ Find the original number.​

Answer 1

Let the numerator of the rational number be X.

Then, the denominator of the rational number = X + 3

According to the question,

• New denominator, after it is increased by 20, = X + 3 + 20 = X +23

• Numerator after it becomes three times = 3 X

Now, According to the question,

• $\frac{3 X}{X + 23} = \frac{1}{8}$

• Or, 8 (3 X) = 1 (X + 23)      {Cross Multiplication}

• Or, 24 X = X + 23

• Or, 24 X - X = 23

• Or, 23 X = 23

• Or, X = 23/23

• Or, X = 1

Now, the original number should be,

= $\frac{ X}{X + 3}$

$=\frac{1 }{1+ 3}$

$= \frac{1}{4}$  (Required Number)

Therefore, 1/4 is the original number.