Question

If 3 is added to the numerator of a fraction it becomes 5/6. If 5 is added to the numerator
and 4 to the denominator, the fraction 3/4.Find the fraction​

Answer 1

Numerator =x
Denominator =y
So, in first part
Numerator = x+3.
Denominator = y.
We get, x+3/y=5/6
=> 5y-6x=18 ( eq 1 ).
So, second part.
Numerator =x+5
Denominator=y+4.
x+5/y+4= 3/4
Now, we get
4*(x+5)=3*(y+4)
Which gives,
4x+20=3y+12
3y-4x=8 ( eq 2)
The equations are.
5y-6x=18 (eq1)
3y -4x=8 (eq2)
By substitution method,
From (eq1) we get,
(18+6x)/5=y (eq3)
Putting the value of (eq3) in (eq2)
We get, 3*(18+6x)/5-4x=8
=> 54+18x-20x=40.
=> x=14/2
=>x=7.
Putting value of x in (eq1)
5y-6*7=18.
=> 5y= 60
=> y = 12.

Answer 2

here is step- by- step solution