The numerator of a fraction is less than its denominator by 5. When the numerator becomes three times and the denominator gets increased by 10, the fraction becomes 3/4. Find the fraction.
Please do step by step explanation.
Answers
Step-by-step explanation:
numerator be x
denominator = x+5
accordingly,
3x/x+15 = 3/4
12x= 3x+45
9x = 45
x = 5
numerator = 5
denominator = 10
5/10 is the answer.
Step-by-step explanation:
Given :-
The numerator of a fraction is less than its denominator by 5. When the numerator becomes three times and the denominator gets increased by 10, the fraction becomes 3/4.
To find :-
Find the fraction ?
Solution :-
Let the denominator of a fraction be X
The numerator of the fraction
= less than its denominator by 5
= X-5
The Original fraction
= Numerator/Denominator
= (X-5)/X
If the denominator is increased by 10 then it will becomes (X+10)
Three times the numerator =3(X-5)
Given that
The numerator becomes three times and the denominator gets increased by 10 then the fraction = 3/4
=> 3(X-5)/(X+10) = 3/4
On applying cross multiplication then
=> 4×3(X-5) = 3×(X+10)
On cancelling 3 both sides then
=> 4(X-5) = X+10
=> 4X-20 = X+10
=> 4X-X = 10+20
=> 3X = 30
=> X = 30/3
=> X = 10
The denominator = 10
The numerator = X-5
= 10-5
The numerator = 5
The fraction = 5/10
Answer:-
The required fraction for the given problem is 5/10
Check:-
The numerator = 5
The denominator = 10
denominator -5 = 10-5 = 5 = Numerator
and
3 times the numerator = 3×5 = 15
Denominator+10 = 10+10 = 20
The new fraction = 15/20
=> (5×3)/(5×4)
=> 3/4
Verified the given relations in the given problem.