the denominator of fraction is 2 more than the numerator. If 3 is added to both, numerator and the denominator, the fraction becomes 3/4 . what is the fraction
Answers
Step-by-step explanation:
Given :-
The denominator of fraction is 2 more than the numerator.If 3 is added to both, numerator and the denominator, the fraction becomes 3/4 .
To find :-
What is the fraction?
Solution :-
Let the numerator of a fraction be X
Then the denominator = 2 more than the numerator.
=> Denominator = Numerator + 2
=> Denominator = X+2
Now the Original Fraction = X/(X+2) ----(1)
If 3 is added to both numerator and the denominator then it becomes
=> (X+3)/(X+2+3)
=> (X+3)/(X+5)
According to the given problem
If 3 is added to both, numerator and the denominator, the fraction becomes 3/4
=> (X+3)/(X+5) = 3/4
On applying cross multiplication then
=> 4(X+3) = 3(X+5)
=> 4X+12 = 3X+15
=> 4X-3X = 15-12
=> X = 3
=> Numerator = 3
Denominator = Numerator + 2
=> Denominator = 3+2 = 5
Fraction = Numerator/Denominator
Fraction = 3/5
Answer:-
The Original Fraction for the given problem is 3/5
Check :-
Fraction = 3/5
Denominator = 3+2 = 5
Denominator = Numerator + 2
If 3 is added to both, numerator and the denominator, the fraction becomes
=> (3+3)/(5+3)
=> 6/8
=> 3/4
Verified the given relations in the given problem.
Used formula:-
Fraction = Numerator / Denominator