A fraction F becomes 1/2 when its denominator is increased by 4 and becomes 1/3 when its
numerator is decreased by 5. Then F equals _______. please tell correctly step by step
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Answers
Step-by-step explanation:
Given:-
A fraction F becomes 1/2 when its denominator is increased by 4 and becomes 1/3 when its
numerator is decreased by 5
To find:-
Find the fraction F?
Solution:-
Let the required fraction F be X/Y
Let the numerator be X
and the denominator be Y
Given that
The fraction F becomes 1/2 when its denominator is increased by 4
=> X/ (Y+4) = 1/2
On applying cross multiplication then
=> 2X = (Y+4)
=> 2X -4 = Y
Y = 2X-4 ----------(1)
and
The fraction F becomes 1/3 when its numerator is decreased by 5
=> (X-5)/Y = 1/3
On applying cross multiplication then
=> 3(X-5) = Y
=>3X-15 = Y --------(2)
On Substituting the value of Y in (2) from (1)
=> 3X-15= 2X-4
=> 3X-2X = 15-4
=> X = 11
On Substituting the value of X in (1) then
Y = 2(11)-4
=> Y = 22-4
=> Y = 18
X/Y = 11/18
The fraction F = 11/18
Answer:-
The required fraction for the given problem is F = 11/18
Check:-
The fraction F = 11/18
The fraction F becomes 1/2 when its denominator is increased by 4
=> 11/(18+4)
=> 11/22
=> 1/2
Verified the given relation.
and
The fraction F becomes 1/3 when its numerator is decreased by 5
=>(11-5)/18
=> 6/18
=> 1/3
Verified the given relation.