The denominator of a fraction is 2 more than the numerator. If 1 is added to both the numerator and denominator, the fraction becomes 1/2 . What is the fraction ? (Use two variables)
Answers
Given :-
The denominator of a fraction is 2 more than the numerator.
If 1 is added to both the numerator and denominator, the fraction becomes 1/2 .
To find :-
The fraction .
Solution :-
Let the numerator be X
Let the denominator be Y
The fraction = Numerator/Denominator = X/Y
The denominator = 2 more than the numerator.
=> Y = X+2
=> Y-X = 2
=> -X+Y = 2
=> X-Y = -2 -------------(1)
If 1 is added to the numerator then it will be X+1
If 1 is added to the denominator then it will be Y+1
Then the new fraction = (X+1)/(Y+1)
According to the given problem
The new fraction = 1/2
Therefore, (X+1)/(Y+1) = 1/2
On applying cross multiplication then
=> 2(X+1) = 1(Y+1)
=> 2X+2 = Y+1
=> 2X-Y = 1-2
=> 2X-Y = -1 -------------(2)
On subtracting (1) from (2) then
2X-Y = -1
X -Y = -2
(-)
__________
X + 0 = +1
__________
Therefore, X = 1
The numerator = 1
On substituting the value of X in (1) then
1-Y = -2
=> 1+2 = Y
=> Y = 3
The denominator = 3
Therefore, The fraction = 1/3
Answer :-
The required fraction is 1/3
Check :-
The numerator = 1
The denominator = 3 = 1+2
The denominator = The numerator + 2
The denominator of the fraction is 2 more than the numerator.
On adding 1 to both numerator and denominator then the fraction will be (1+1)/(3+1) = 2/4 = 1/2
Verified the given relations in the given problem.
Step-by-step explanation:
Given :-
The denominator of a fraction is 2 more than the numerator.
If 1 is added to both the numerator and denominator, the fraction becomes 1/2 .
To find :-
The fraction .
Solution :-
Let the numerator be X
Let the denominator be Y
The fraction = Numerator/Denominator = X/Y
The denominator = 2 more than the numerator.
=> Y = X+2
=> Y-X = 2
=> -X+Y = 2
=> X-Y = -2 -------------(1)
If 1 is added to the numerator then it will be X+1
If 1 is added to the denominator then it will be Y+1
Then the new fraction = (X+1)/(Y+1)
According to the given problem
The new fraction = 1/2
Therefore, (X+1)/(Y+1) = 1/2
On applying cross multiplication then
=> 2(X+1) = 1(Y+1)
=> 2X+2 = Y+1
=> 2X-Y = 1-2
=> 2X-Y = -1 -------------(2)
On subtracting (1) from (2) then
2X-Y = -1
X -Y = -2
(-)
__________
X + 0 = +1
__________
Therefore, X = 1
The numerator = 1
On substituting the value of X in (1) then
1-Y = -2
=> 1+2 = Y
=> Y = 3
The denominator = 3
Therefore, The fraction = 1/3
Answer :-
The required fraction is 1/3
Check :-
The numerator = 1
The denominator = 3 = 1+2
The denominator = The numerator + 2
The denominator of the fraction is 2 more than the numerator.
On adding 1 to both numerator and denominator then the fraction will be (1+1)/(3+1) = 2/4 = 1/2
Verified the given relations in the given problem.