a fraction becomes 9/11 7 if 2 is added to both numerator and denominator if 1 is subtracted to more than number and discriminator it become 3 by 2 find the fraction
Answers
Answer:
Let the fraction be x/y.
(x+2)/(y+2) = 9/11, or
9y+18 = 11x+22
9y = 11x+4, or
45y = 55x+20 …(1)
(x+3)/(y+3) = 5/6, or
5y+15 = 6x+18, or
5y = 6x+3, or
45y = 54x+27 …(2)
Equate (1) and (2)
55x+20 = 54x+27
x = 7
Again, 9y = 11x+4, or
9y = 77 + 4 or
y = 81/9 = 9
The fraction is (7/9). Answer
To find the fraction.
EXPLANATION.
Case = 1.
Let the numerator of the fraction be = ( x + 2 )
Let the denominator of the fraction be = ( y + 2 )
Fraction become = 9/11
=> x + 2 / y + 2 = 9/11
=> 11 ( x + 2 ) = 9 ( y + 2 )
=> 11x + 22 = 9y + 18
=> 11x - 9y = -4 .........(1)
Case = 2.
if 1 is subtracted to both numerator and
denominator it become 3/2
=> x - 1 / y - 1 = 3/2
=> 2 ( x - 1 ) = 3 ( y - 1 )
=> 2x - 2 = 3y - 3
=> 2x - 3y = -1 .......(2)
From equation (1) and (2) we get,
=> multiply equation (1) by 1
=> multiply equation (2) by 3
we get,
=> 11x - 9y = -4
=> 6x - 9y = -3
=> 5x = -1
=> x = -1/5
put the value of x = -1/5 in equation (1)
we get,