Question

The numerator of a rational number is less than its denominator by 3. If the numerator becomes 3 times and the denominator is increased by 20, the new number becomes 1/8. Find the original number.??

Answer 1

the numerator of a rational number is less than its denominator by 3.if the numerator became 3 times and the denominator is increased by 20,the faction became 1\8,find the original faction 
.
Let d = denominator
then
d-3 = numerator
.
3(d-3)/(d+20) = 1/8
(3d-9)/(d+20) = 1/8
cross multiplying:
8(3d-9) = (d+20)

24d-72 = d+20
23d-72 = 20
23d = 92
d = 4 (denominator)
.
numerator:
d-3 = 4-3 = 1
.
answer: 1/4 

Answer 2

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Let denominator be x

Since we are given that e numerator of a rational number is less than its denominator by 3.

So, numerator = x-3

So, fraction = $\frac{x-3}{x}$

Now, the numerator becomes 3 times and the denominator is increased by 20, the new number becomes 1/8.

$\frac{3(x-3)}{x+20} =\frac{1}{8}$

$\frac{3x-9}{x+20} =\frac{1}{8}$

Now cross multiplying

$(3x-9)*8=x+20$

$24x-72=x+20$

$24x-x=x+20+72$

$23x=92$

$x=4$

So, putting value of x in 1 get the original fraction .

fraction = $\frac{4-3}{4}$

fraction = $\frac{1}{4}$