A fraction becomes 9/11 if 2 is added to both numerator and denominator. if 3 is added to both numerator and denominator it becomes 5/6 find the fraction by substitution method
Answers
(x+2)/(y+2)=9/11
or, 11x+22=9y+18
or, 11x-9y=18-22
or, 11x-9y=-4
or, 11x=9y-4
or, x=(9y-4)/11
and, (x+3)/(y+3)=5/6
or, 6x+18=5y+15
or, 6x-5y=15-18
or, 6(9y-4)/11-5y=-3
or, (54y-24-55y)11=-3
or, -y-24=-3×11
or, y+24=33
or, y=33-24=9
then, x=(9×9-4)/11
or, x=(81-4)/11
or, x=77/11=7
∴, x=7,y=9 and the fraction is :7/9
Answer:
Step-by-step explanation:
Information :- This solution is based on Cross Multiplication.
Given :-
Fraction becomes 9/11 if 2 is added to both numerator and denominator.
If 3 is added to both numerator and denominator it becomes 5/6.
Solution :-
Let the Numerator be x
Let the Denominator be y
Fraction = x/y
According to the Question,
⇒ (x + 2)/y + 2 = 9/11
On Cross multiplying,
⇒ 11x + 22 = 9y + 18
Subtracting 22 from both sides,
⇒ 11x = 9y – 4
Dividing by 11, we get
⇒ x = 9y – 4/11 … (i)
Then,
⇒ (x+3)/y +3 = 5/6 … (ii)
On Cross multiplying,
⇒ 6x + 18 = 5y + 15
Subtracting the value of x, we get
⇒ 6(9y – 4 )/11 + 18 = 5y + 15
Subtracting 18 from both the sides
⇒ 6(9y – 4 )/11 = 5y – 3
⇒ 54 – 24 = 55y – 33
⇒ –y = – 9
⇒ y = 9
Putting this value of y in equation (i), we get
⇒ x = 9y – 4
⇒ x = (81 – 4)/77
⇒ x = 77/11
⇒ x = 7
Hence, the fraction is 7/9.