Question

the numerator of a rational number is less than its denominator by 3 if the number become there times and the denominater is incresesed by 20 the new number become 1\8 find the original number
​

Answer 1

Answer:

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}

x

x−3

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}

x+20

3(x−3)

=

8

1

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

x+20

3x−9

=

8

1

Now cross multiplying

(3x-9)*8=x+20(3x−9)∗8=x+20

24x-72=x+2024x−72=x+20

24x-x=x+20+7224x−x=x+20+72

23x=9223x=92

x=4x=4

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

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

4

4−3

fraction = \frac{1}{4}

4

1