Ex 3.3 Q2 (i) - If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
Solution:- Numerator = x
Denominator = y
∴ Fraction =
x
/
y
Case (i): Given that, if we add 1 to the numerator and subtract 1 from the denominator, fraction becomes 1,
∴
x + 1
/
y - 1
= 1 ∴ x + 1 = 1(y - 1)
∴ x + 1 = y - 1
∴ x = y - 1 - 1
∴ x = y - 2 ------- (i)
Case (ii): Given that, if we add 1 to the denominator only, it becomes 1/2,
∴
x
/
y + 1
=
1
/
2
∴ 2(x) = 1(y + 1)
∴ 2x = y + 1
∴ 2(y - 2) = y + 1 ----- { from (i) }
∴ 2y - 4 = y + 1
∴ 2y - y = 1 + 4
∴ y = 5
➙ Putting y = 5 in Eqⁿ(i)
∴ x = 5 - 2
∴ x = 3
Therefore,
*Numerator
= x
= 3
*Denominator
= y
= 5
∴ Fraction =
x
/
y
=
3
/
5
Hence,
The required fraction is 3/5.
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Try This..
✒ The sum of the numerator and denominator of a fraction is 11. If the numerator is increased by 2 and the denominator is increased by 3, the fraction becomes 2/3. Find the original fraction.
✒ A number consists of two digits. If the digits are reversed, the number increases by 27. The sum of the digits is 9. Find the number.
✒ If the numerator of a fraction is increased by 2 and the denominator is decreased by 1, the fraction becomes 2. If the numerator is decreased by 1 and the denominator is increased by 2, it becomes 1/2. Find the fraction.
❌ Common Mistakes
Not defining variables properly:▸ Always begin by clearly assuming the variables (x = numerator, y = denominator).Wrong equation setup:▸ Carefully convert the words into equations. A small mistake can throw the whole solution off.Skipping cross-multiplication:▸ Especially in conditions involving fractions, always multiply correctly.Not checking the final answer:▸ Always substitute back to verify if your fraction satisfies both given conditions.
📝 Related Questions:-
- Ex 3.3 Q2 (ii) - Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
- Ex 3.3 Q2 (iii) - The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- Ex 3.3 Q2 (iv) - Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
- Ex 3.3 Q2 (v) - A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Queries Solved:-
Class 10 Ex 3.3
Ex 3.3 Q2 i Class 10
Class 10 Ex 3.3 Q2 i
Class 10 Chap 3 Ex 3.3 Q2 i
Class 10 Pair Of Linear Equations in Two Variables
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