Ex 3.2 Q3 (v) - 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.
Solution:-Let,
Numerator = x
Denominator = y
∴ Fraction =
x
/
y
Case (i): When 2 is added to both the numerator and the denominator, fraction becomes 9/11,
∴
x + 2
/
y + 2
=
9
/
11
∴ 11(x + 2) = 9(y + 2)
∴ 11x + 22 = 9y + 18
∴ 11x - 9y = 18 - 22
∴ 11x - 9y = -4 ------- (1)
Case (ii): When 3 is added to both the numerator and the denominator, fraction becomes 5/6,
∴
x + 3
/
y + 3
=
5
/
6
∴ 6(x + 3) = 5(y + 3)
∴ 6x + 18 = 5y + 15
∴ 6x - 5y = 15 - 18
∴ 6x - 5y = -3 ------- (2)
Hence, our equations are..
11x - 9y = -4 ------- (1)
6x - 5y = -3 ------- (2)
➙ From Eqⁿ(1)
11x - 9y = -4
∴ 11x = 9y - 4
∴ x =
9y - 4
/
11
------- (3)➙ Putting Eqⁿ(3) in Eqⁿ(2)
6(
9y - 4
/
11
) - 5y = -3 ∴ 6(9y - 4) - 5y × 11 = -3 × 11
∴ 54y - 24 - 55y = -33
∴ 55y - 54y = 33 - 24
∴ y = 9
➙ Putting y = 9 in Eqⁿ(3)
∴ x =
9(9) - 4
/
11
=
81 - 4
/
11
=
77
/
11
= 7
∴ x = 7
Therefore,
*Numerator
= x
= 7
*Denominator
= y
= 9
∴ Fraction =
x
/
y
=
7
/
9
Hence,
The required fraction is 7/9.
------------------------------------
Try This..
✒ A fraction becomes 3/4 when 1 is added to both numerator and denominator. If 5 is added to both, it becomes 4/5. Find the fraction.
✒ The sum of the numerator and denominator is 15. If 3 is added to numerator and 2 to the denominator, the fraction becomes 6/7. Find the fraction.
✒ If a fraction becomes 7/8 when 3 is subtracted from numerator and denominator, and 5/6 when 2 is added to both, what is the fraction?
❌ Common Mistakes
Mixing up the fraction format:▸ Always remember it’s x/y, not y/x.Incorrect cross-multiplication:▸ Double-check your expansion during each step if you're using this method.Forgetting signs:▸ Be careful with negative numbers when simplifying.Jumping steps:▸ Always write down each equation clearly to avoid confusion later.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 3.2
Ex 3.2 Q3 v Class 10
Class 10 Ex 3.2 Q3 v
Class 10 Chap 3 Ex 3.2 Q3 v
Class 10 Pair Of Linear Equations in Two Variables
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