5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.
Answers
Correct Question :-
The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
Answer:-
The required rational number is 11/21.
Step-by-step explanation
To Find :-
- The rational number.
★ Solution
Given that,
The denominator of a rational number is greater than it's numerator by 10.
Assumption
Let us assume the numerator & denominator as (x) and (x + 10) respectively.
Also given,
The numerator is increased by 19 and the denominator is decreased by 1. The new rational number is 3/2.
According the question,
Numerator = (x) + 19 = (x + 19)
Denominator = (x + 10) - 1 = (x + 9).
∴ (x + 19)/(x + 9) = 3/2
By simplifying,
⇒ (x + 19)/(x + 9) = 3/2
⇒ 3(x + 9) = 2(x + 19)
⇒ 3x + 27 = 2x + 38
⇒ 3x - 2x + 27 = 38
⇒ 3x - 2x = 38 - 27
⇒ x = 38 - 27
⇒ x = 11
The value of x is 11.
__________________________
Finding, The numerator and denominator-
Numerator :-
We assumed the numerator as (x).
⇒ x
⇒ 11
Denominator :-
We assumed the denominator as (x + 10).
⇒ (x + 10)
⇒ (11 + 10)
⇒ 21
Therefore, The fraction is - 11/21.