20. The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2 Find the rational number.
Answers
Answer:
If a rational number has a numerator three less than the denominator and if numerator and denominator are increased by 2 and 5 respectively, then it becomes 1/2, then the rational number is 4/7
Step-by-step explanation:
Let us take x and y as the numerators and denominators of the rational number respectively
Given
x= y-3 and
if y is increased by 5 and x by 2 then the number formed is 1/2
That is
x= y-3
So,
2x-y = 2(y-3)-y = 2y -6 -y = y-6
So, y-6 = 1
y= 1 +6= 7
So x = y-3 = 7-3 =4
So the rational number is 4/7
Step-by-step explanation:
Given :-
The numerator of a rational number is 3 less than the denominator.
The denominator is increased by 5 and the numerator by 2 then rational number is 1/2.
To find :-
The rational number.
Solution :-
Let the denominator of a rational number be X
Then, The numerator = 3 less than the denominator
=> Numerator = Denominator - 3
=> Numerator = X-3
The Rational number
= Numerator/Denominator
=> The Rational number = (X-3)/X
If the numerator is increased by 2 then it becomes X-3+2 = X-1
If the denominator is increased by 5 then it becomes X+5
Then the rational number = (X-1)/(X+5)
According to the given problem
The new rational number = 1/2
=> (X-1)/(X+5) = 1/2
On applying cross multiplication then
=> 2(X-1) = 1(X+5)
=> 2X-2 = X+5
=> 2X-X = 5+2
=> X = 7
Therefore, Denominator = 7
Numerator = X-3 = 7-3 = 4
The rational number = 4/7
Answer:-
The required rational number is 4/7
Check :-
The numerator = 4
The denominator = 7
=> Numerator = 4
=> Numerator = 7-3
Therefore, Numerator = Denominator - 3
And
If the numerator is increased by 2 then it will be 4+2 = 6
If the denominator is increased by 5 then it will be
7+5 = 12
Then the Rational number will be
6/12 = 1/2
Verified the given relations in the given problem.