Question

A fraction becomes ½ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. if the denominator is 5 more than the numerator , find the fraction.
chapter - simultaneous linear equations​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• A fraction becomes ½ if 5 is subtracted from its numerator and 3 is subtracted from its denominator.

• The denominator is 5 more than the numerator.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The fraction.

$\bf{\underline{\underline\green{Solution:-}}}$

According to the question:-

The denominator is 5 more than the numerator.

Let the numerator be x

The denominator = x + 5

A fraction becomes ½ if 5 is subtracted from its numerator and 3 is subtracted from its denominator.

If 5 is subtracted from the numerator

The numerator = x - 5

If 3 is subtracted from denominator.

The denominator

= (x + 5) - 3

= x + 5 - 3

= x + 2

The fraction becomes ½.

$\rm\implies\dfrac{x - 5}{x + 2} = \dfrac{1}{2}$

By cross multiplication:-

$\rm\implies{2(x - 5)} = {1(x + 2)}$

$\rm\implies{2x - 10} = {x + 2}$

$\rm\implies{2x -x} = { 2 + 10}$

$\rm\implies{x} = { 12}$

The numerator = x = 12

The denominator

= x + 5

= 12 + 5

= 17

$\underline{ \boxed{\rm\therefore The \: fraction = \frac{12}{17} }}$