# Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction. - Mathematics

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

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

#### Solution

Let the fraction be x/y

According to the question,

(x-1)/y = 1/3

⇒ 3x - y = 3... (i)

x/(y+8) = 1/4

⇒ 4x - y = 8 ... (ii)

Subtracting equation (i) from equation (ii), we get

x = 5 ... (iii)

Putting this value in equation (i), we get

15 - y = 3

y = 12

Hence, the fraction is 5/12

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 4.2 | Page 63