when we add 6 to numerator of a fraction and simplyfy it we get 1/2 when we dd 7 to denominator of same fraction we get 1/3 what's the orginal fraction?
Answers
Answer:
The original fraction is 19/50.
Step-by-step explanation:
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Step-by-step explanation:
Solution :-
Let the Numerator be X
Let the Denominator be Y
Then the fraction = X/Y
If we add 6 to the numerator then the fraction will be (X+6)/Y
According to the given problem
The new fraction = 1/2
=> (X+6)/Y = 1/2
On applying cross multiplication then
=> 2(X+6) = Y
=> 2X+12 = Y
=> 2X - Y = -12 ----------------(1)
and
If we add 7 to the denominator then the fraction will be X/(Y+7)
According to the given problem
The new fraction = 1/3
=> X/(Y+7) = 1/3
On applying cross multiplication then
=> 3X = Y+7
=> 3X-Y = 7 ----------(2)
On Subtracting (1) from (2)
3X-Y = 7
2X-Y = -12
(-)
________
X + 0 = 19
________
=>X = 19
=> Numerator = 19
On Substituting the value of X in (1) then
2(19)-Y = -12
=> 38-Y = -12
=> -Y = -12-38
=> - Y = -50
=> Y = 50
The Denominator = 50
The fraction = 19/50
Answer:-
The original fraction for the given problem is 19/50
Check :-
The fraction = 19/50
On adding 6 to the numerator then
=> (19+6)/50
=> 25/50
=> 1/2
and
on adding 7 to the denominator then
=> 19/(50+7)
=> 19/57
=> 1/3
Verified the given relations in the given problem.