Question

the denominator of a rational number is greater than the numerator by 5. if 1 is subtracted from the numerator and 3 is added ro the denominator,the new number become¼. find the original number.​

Answer 1

Step-by-step explanation:

d = n +5

{n-1 }/d+3 = 1/4

4n-4 = d+3

4n-d =7

4n-n-5 =7

3n = 12

n =4

d = 16-7

d = 9

Answer 2

Answer :-

• Original Number = 4/9.

Explanation :-

Given : The denominator of a rational number is greater than the numerator by 5. When 1 is subtracted from the numerator and 3 is added to the denominator then the new number becomes 1/4.

To Find : The Original number.

Solution :

Let, the numerator be x.

So, the denominator will become x + 5.

According to the question,

⇒ (x - 1)/(x + 5 + 3) = 1/4.

⇒ (x - 1)/(x + 8) = 1/4.

⇒ 4(x - 1) = x + 8

⇒ 4x - 4 = x + 8

⇒ 4x - x = 8 + 4

⇒ 3x = 12

⇒ x = 12 ÷ 3.

⇒ x = 4.

Therefore,

• Numerator = x = 4.
• Denominator = x + 5 = 9.

So, Original Fraction = 4/9.