Question

the numerator of a rational number is less than its denominator if the numerator is multiplied by 3 and denominator is increased by 20 then the new ration number is 1/8 find the original number​

Answer 1

Correct 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

Solution :

• The numerator of a rational number is less than its denominator by 3

Let denominator be x

So , Numerator = x - 3

So , Fraction = ( x - 3 ) / x

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

➠ $\sf \dfrac{3(x-3)}{x+20}=\dfrac{1}{8}$

➠ 8 [ 3 ( x - 3 ) ] = 1 ( x + 20 )

➠ 24 ( x - 3 ) = x + 20

➠ 24x - 72 = x + 20

➠ 24x - x = 20 + 72

➠ 23x = 92

➠ x = 92/23

➠ x = 4

Numerator : 1

➳ x - 3 = 4 - 3 = 1

Denominator : 4

➳ x = 4

Original number =  $\sf \dfrac{1}{4}\ \; \pink{\bigstar}$

Answer 2

Ans is 1/4

Explanation:

Let the numerator of the rational number be x. 

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

According to the given condition,

New numerator =3x and new denominator =(x+3)+20=x+23

By cross multiplying, we get

8(3x)=x+23

⇒24x=x+23

⇒23x=23 ....[On Transposing]

x=1

Therefore, numerator of the rational number =1 and denominator =1+3=4.

hence the original rational num is 1/4