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:-
- Ex 3.2 Q2 - Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.
- Ex 3.2 Q3 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.
- Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Ex 3.2 Q3 (iii) - The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
- Ex 3.2 Q3 (iv) - The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
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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