# the sum of the numerator and denominator of a fraction is 12

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## The sum of the numerator and the denominator of a fraction is 12 . If the denominator is increased by 3 , the fraction becomes 1 / 2. Find the fractions.

The sum of the numerator and the denominator of a fraction is 12 . If the denominator is increased by 3 , the fraction becomes 1 / 2. Find the fractions.

Byju's Answer Standard X Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

The sum of th... Question

The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fractions.

Open in App Solution

Let numerator = x and denominator = y

From the given conditions, we have:

x + y = 12 ... (1) x/y+3 = 1/2 2x - y = 3 ... (2)

Adding (1) and (2), we get,

3x = 15 or x = 5 So, y = 12 - 5 = 7

Thus, the fraction is 5/7.

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SIMILAR QUESTIONS

**Q.**The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

**Q.**

The sum the numerator and denominator of a fraction is 12 if the denominator is increased by 3 the fraction becomes 1\2 find the fraction

**Q.**

The sum of the numerator and denominator of a fraction is 12. If the denominator is incresed by 3, the fraction becomes 1/2. Find the fraction.

**Q.**Sum of the numerator and the denominator of a fraction is 12. If the denominator is increared by 3 then fraction becomes 1/2. Find the fraction.

**Q.**In a fraction, if numerator is increased by 2 and denominator is decreased by 3, then the fraction becomes 1. Instead, if numerator is decreased by 2 and denominator is increased by 3, then the fraction becomes

3 8

. Find the fraction.

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Elimination Method of Finding Solution of a Pair of Linear Equations

Standard X Mathematics

## The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

Q.11 of chapter 3, 3. Pair of Linear Equations in Two Variables - RD Sharma - Mathematics book. The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

11

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

Let the numerator be ‘a’ and denominator be ‘b’.

Given, sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.

⇒ a + b = 12 ------ (1)

Also, a/(b + 3) = 1/2

⇒ 2a – b = 3 ------- (2)

Adding eq1 and eq2

⇒ a + b + 2a – b = 15

⇒ 3a = 15 ⇒ a = 5 Thus, b = 7 Fraction is 5/7.

## The Sum of the Numerator and Denominator of a Fraction is 12. If the Denominator is Increased by 3, the Fraction Becomes 1/2. Find the Fraction.

The Sum of the Numerator and Denominator of a Fraction is 12. If the Denominator is Increased by 3, the Fraction Becomes 1/2. Find the Fraction.

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The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

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### SOLUTION

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is

xy

The sum of the numerator and denominator of the fraction is 12. Thus, we have

x+y=12 ⇒x+y-12=0

If the denominator is increased by 3, the fraction becomes

12 . Thus, we have xy+3=12 ⇒2x=y+3 ⇒2x-y-3=0

So, we have two equations

x+y-12=0 2x-y-3=0

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

x1×(-3)-(-1)×(-12)=-y1×(-3)-2×(-12)=11×(-1)-2×1

⇒x-3-12=-y-3+24=1-1-2

⇒x-15=-y21=1-3 ⇒x15=y21=13 ⇒x=153,y=213 ⇒x=5,y=7

Hence, the fraction is

57

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables

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Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.8 [Page 89]

Q 11 Q 10 Q 1

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RD Sharma Class 10 Maths

Chapter 3 Pair of Linear Equations in Two Variables

Exercise 3.8 | Q 11 | Page 89

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