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# Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method 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? - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Elimination Method

#### Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method

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

Let the fraction be x/y

According to the given information,

(x+1)/(y-1)=1 ⇒ x - y = -2  (1)

x/(y+1) = 1/2 ⇒ 2x-y = 1   (2)

Subtracting equation (1) from equation (2), we obtain

x = 3 (3)

Substituting this value in equation (1), we obtain

3 - y = -2

-y = -5

y = 5

Hence the fraction is 3/5

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 3: Pair of Linear Equations in Two Variables
Ex. 3.40 | Q: 2.1 | Page no. 57

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Solution Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method 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? Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method.
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