a fraction becomes 9/11 if 2 s added to both the numerator and the denominator if 3 is added to both the numerator and denominator it becomes 5/6 find the fraction
Answers
Answer:
a fraction becomes 9/11 if 2 s added to both the numerator and the denominator if 3 is added to both the numerator and denominator it becomes 5/6 find the fraction
Step-by-step explanation:
Given :-
A fraction becomes 9/11 if 2 s added to both the numerator and the denominator if 3 is added to both the numerator and denominator it becomes 5/6.
To find :-
Find the fraction ?
Solution :-
Let the numerator be X
Let the denominator be Y
Then, the fraction = X/Y
If 2 is added to both numerator and denominator then they will be X+2 and Y+2
They the fraction = (X+2)/(Y+2)
According to the given problem
The fraction = 9/11
=> (X+2)/(Y+2) = 9/11
On applying cross multiplication then
=> 11(X+2) = 9(Y+2)
=> 11X+22 = 9Y+18
=> 11X-9Y = 18-22
=> 11X-9Y = -4 --------------(1)
If 3 is added to both numerator and denominator then they will be X+3 and Y+3
They the fraction = (X+3)/(Y+3)
According to the given problem
The fraction = 5/6
=> (X+3)/(Y+3) = 5/6
On applying cross multiplication then
=> 6(X+3) = 5(Y+3)
=> 6X+18 = 5Y+15
=> 6X-5Y = 15-18
=> 6X-5Y = -3 --------------(2)
On multiplying (1) with 6 then
66X-54Y = -24 -------------(3)
On multiplying (2) with 11 then
66X-55Y = -33 ------------(4)
In Subtracting (3) from (4) then
=> (4)-(3)
66X-55Y = -33
66X-54Y = -24
(-) (+) (+)
____________
0 -Y = - 9
____________
=> -Y = -9
=> Y = 9
So the denominator = 9
On Substituting the value of Y in (1)
=> 11X-9(9) = -4
=> 11X -81 = -4
=> 11X = -4+81
=> 11X = 77
=> X = 77/11
=> X = 7
The numerator = 7
The fraction = 7/9
Answer:-
The required fraction for the given problem is 7/9
Check:-
The fraction = 7/9
If 2 is added to both numerator and denominator then
=> (7+2)/(9+2)
=> 9/11
and
If 3 is added to both numerator and denominator then
=> (7+3)/(9+3)
=>10/12
=> 5/6
Verified the given relations in the given problem.