# The Numerator of a Fraction is 4 Less than the Denominator. If the Numerator is Decreased by 2 and Denominator is Increased by 1, Then the Denominator is Eight Times the Numerator. Find the Fraction. - Mathematics

Definition

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

#### Solution

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

The numerator of the fraction is 4 less the denominator. Thus, we have

x = y -4

 ⇒ x -y =-4

If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is 8 times the numerator. Thus, we have

 y + 1 = 8(x-2)

⇒ y + 1= 8x -16

 ⇒ 8x -y = 1+16

⇒ 8x - y =17

So, we have two equations

 x - y = -4

 8x -y =17

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

Subtracting the second equation from the first equation, we get

( x -y)-(8x -y)=-4-17

⇒ x - y -8x +y =-21

 ⇒ -7 x =-21

 ⇒ 7 x =21

 ⇒ x =21/7

 ⇒ x = 3

Substituting the value of in the first equation, we have

 3- y =-4

⇒ y = 3+4

 ⇒ y = 7
Hence, the fraction is 3/7

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.8 | Q 1 | Page 88