Question

The numerator of a rational number is 8 less than it's denominator. If the numerator is multiplied by 3 and
10 is added to the denominator the new rational number is 21/25.Find the original rational number.​

Answer 1

Answer:

original rational number = 7/15

Step-by-step explanation:

Let the denominator of a rational number be x

then

numerator of a rational number be (x-8)

Then,

Rational number become= { (x-8) / x }

Next,

Numerator multiplied by 3

so, numerator = 3×(x-8)

10 is added to denominator.

so, denominator = (x+10)

Rational number become = {3×(x-8) / ( x+10 )}

According to question,

3×(x-8) / ( x+10 ) = 21/25

now, the trick is to compare the denominators on both sides.

we get:

x+10 = 25

x = 25 -10

x = 15.

So, original rational number become

{(15-8)/15 } =7/15

You can check the answer also,

(7 ×3) / (15 +10) = 21/25

which shows our answer is correct.