A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
Answers
Let the fraction be x/y.
According to the question,
(x + 2)/(y + 2) = 9/11
11x + 22 = 9y + 18
11x – 9y = -4 …………….. (1)
(x + 3)/(y + 3) = 5/6
6x + 18 = 5y +15
6x – 5y = -3 ………………. (2)
From (1), we get
x = (-4 + 9y)/11 …………….. (3)
Substituting the value of x in (2), we get
6[(-4 + 9y)/11] – 5y = -3
-24 + 54y – 55y = -33
-y = -9
y = 9 ………………… (4)
Substituting the value of y in (3), we get
x = (-4 + 81)/11 = 77/11 = 7
Hence, the fraction is 7/9.
Answer:
7/9
Step-by-step explanation:
Let the digit at numerator be x
and digit at denominator be y
fraction=x/y
case - I
x+2/y+2=9/11
11(x+2)=9(y+2) (by cross multiplication)
11x+22=9y+18
11x-9y=18-22
11x-9y=-4 _____(i)
case - II
x+3/y+3=5/6
6(x+3)=5(y+3) ( by cross multiplication)
6x+18=5y+15
6x-5y=15-18
6x-5y=-3 ______(ii)
from eq(i) &eq(ii)
6(11x-9y=-4)
11(6x-5y=-3)
substract
66x-54y=-24
66x-55y=-33
__________
y=9 put in eq (i)
11x-9*9=-4
11x=-4+81
11x=77
x=77/11
x=7
therefore, fraction=x/y
=7/9