If 2 is subtracted from numerator of a fraction then the fraction becomes 1/3 but if 1 is added to its denominator then the fraction becomes 1/2 . find the fraction
Answers
Step-by-step explanation:
Given :-
2 is subtracted from numerator of a fraction then the fraction becomes 1/3 but if 1 is added to its denominator then the fraction becomes 1/2 .
To find:-
Find the fraction ?
Solution:-
Let the numerator be X
Let the denominator be Y
Then,the fraction = X/Y
If 2 is subtracted from numerator of a fraction then the fraction becomes 1/3
=> (X-2)/Y = 1/3
On applying cross multiplication then
=> 3×(X-2) = Y×1
=> 3(X-2) = Y
=> 3X-6 = Y
Y = 3X-6 -------------(1)
if 1 is added to its denominator then the fraction becomes 1/2 .
=> X/(Y+1) = 1/2
On applying cross multiplication then
=> 2×X = (Y+1)×1
=> 2X = Y+1
=> Y+1 = 2X
Y = 2X-1 ------------(2)
From (1)&(2)
=> 3X-6 = 2X-1
=> 3X-2X = 6-1
=> X = 5
On Substituting the value of X in (2) then
Y = 2(5)-1
=> Y = 10-1
=>Y = 9
Therefore, X = 5 and Y = 9
The fraction = 5/9
Answer:-
The required fraction for the given problem is 5/9
Check:-
The fraction = 5/9
If 2 is subtracted from numerator of a fraction then the fraction becomes 1/3
=> (5-2)/9
=>3/9
=>1/3
if 1 is added to its denominator then the fraction becomes 1/2 .
=> 5/(9+1)
=> 5/10
=>1/2
Verified the given relations.
are you in Dav school Adambakkam
if yes what's ur name
and class and sec?