when 1 is added to the numerator as well as well he denominator of a certain fraction it becomes 3/5 if 1 is subtracted from both the numerator and the denominator it becomes 1/2 find the fraction
Answers
Given :-
If 1 is added to both numerator and denominator of a fraction then it becomes 3/5.
If 1 is subtracted from both numerator and denominator then it becomes 1/2.
To find :-
The fraction
Solution :-
Let the numerator be X
Let the denominator be Y
The fraction = X/Y
Condition -1 :-
If 1 is added to both numerator and denominator of a fraction it becomes 3/5.
Therefore, (X+1)/(Y+1) = 3/5
On applying cross multiplication then
=> 5(X+1) = 3(Y+1)
=> 5X+5 = 3Y+3
=> 5X-3Y = 3-5
=> 5X - 3Y = -2 ---------(1)
Condition -2:-
If 1 is subtracted from both numerator and denominator of a fraction it becomes 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 multiplying (2) with 3 then
6X-3Y = 3 ---------------(3)
On subtracting (1) from (3)
6X-3Y = 3
5X-3Y = -2
(-)
__________
X + 0 = 5
__________
Therefore, X = 5
On substituting the value of X in (2) then
2(5)-Y = 1
=> 10-Y = 1
=> -Y = 1-10
=> -Y = -9
=> Y = 9
The numerator = 5
The denominator = 9
The fraction = 5/9
Answer :-
The original fraction = 5/9
Check :-
The numerator = 5
The denominator = 9
The fraction = 5/9
If 1 is added to both numerator and denominator of a fraction it becomes (5+1)/(9+1) = 6/10 = 3/5
If 1 is subtracted from both the numerator and the denominator it becomes (5-1)/(9-1) = 4/8 = 1/2
Verified the given relations in the given problem.