3. A fraction becomes 9/11,
if 2 is added to both the numerator and denominator. If 3 is added to
both the numerator and denominator it becomes
5/6
Find the fraction.
Answers
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.
Answer:
Let the numerator and denominator be x and y respectively.
Therefore, the required fraction will be x/y
According to Question now,
➳ (x + 2)/(y + 2) = 9/11
➳ 11(x + 2) = 9(y + 2)
➳ 11x + 22 = 9y + 18
➳ 22 - 18 = 9y - 11x
➳ 4 = 9y - 11x
➳ 11x = 9y - 4
➳ x = 9y - 4/11.......[Equation (i)]
Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]
➳ (x + 3)/(y + 3) = 5/6
➳ (x + 3)6 = 5(y + 3)
➳ 6x + 18 = 5y + 15
➳ 6x - 5y + 18 - 15 = 0
➳ 6x - 5y + 3 = 0
➳ 6(9y - 4)/11 - 5y + 3 = 0
➳ 54y - 24/11 = 5y - 3
➳ 54y - 24 = 11(5y - 3)
➳ 54y - 24 = 55y - 33
➳ -24 + 33 = 55y - 54y
➳ 9 = y
Now, Putting y = 9 in equation (i) we get,
➳ x = 9y - 4/11
➳ x = 9(9) - 4/11
➳ x = 81 - 4/11
➳ x = 77/11
➳ x = 7
Therefore, the required fraction is 7/9.