In a fraction twice the numerator is 2 more than the denominator .if 3 is added to the numerator and to the denominator the new fraction is 2/3 .find the original fraction
Answers
Step-by-step explanation:
Given:-
In a fraction twice the numerator is 2 more than the denominator .if 3 is added to the numerator and to the denominator the new fraction is 2/3 .
To find :-
Find the original fraction ?
Solution :-
Let the denominator in a fraction be Y
Let the numerator of the fraction be X
Then the fraction = X/Y
Given that
Twice the numerator = 2 more than the denominator
=> 2X = Y+2
=> Y = 2X-2 -----------(1)
and
If 3 is added to the numerator and to the denominator the new fraction = 2/3
=> (X+3)/(Y+3) = 2/3
On applying cross multiplication then
=> 3(X+3) = 2(Y+3)
=>3(X+3) = 2(2X-2+3)
=> 3X+9 = 4X-4+6
=> 3X+9 = 4X+2
=>4X+2 = 3X+9
=>4X-3X = 9-2
=> X = 7
On Substituting the value of X in (1) then
Y = 2(7)-2
=> Y = 14-2
=> Y = 12
Therefore fraction = 7/12
Answer:-
The required fraction for the given problem is 7/12
Check:-
The fraction = 7/12
Twice the numerator =2×7 = 14
2 more than the denominator = 12+2 = 14
Twice the numerator is equal to 2 more than the denominator
and
If 3 is added to the numerator and to the denominator the new fraction
= (7+3)/(12+3)
= 10/15
= (2×5)/(3×5)
= 2/3
If 3 is added to the numerator and to the denominator the new fraction = 2/3
Verified the given relations in the given problem.