Question

The numerator of a fraction is 6 less
than the denominatos. If 1 is added
to both numeratos and denominatos,
it becomes half, then find the for
fraction​

Answer 1

Given,

• The numerator of a fraction is 6 less than the denominator .
• When we 1 is added to the both numerator and denominator then its becomes 1/2 .

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be x

And Suppose the denominator be y

Therefore,

$\boxed{\bold{\red{The \ Farction = \dfrac{x}{y}}}}$

According to the First Condition :-

• The numerator of a fraction is 6 less than the denominator .

$\implies \boxed{\sf{x = y - 6}}$

According to the First Condition :-

• When we 1 is added to the both numerator and denominator then its becomes 1/2 .

$\implies \sf{\dfrac{x + 1}{y + 1} = \dfrac{1}{2}}$

$\implies \sf{2(x + 1) = 1(y + 1)}$

$\implies \sf{2x + 2 = y + 1}$

$\implies \sf{2x - y = 1 - 2}$

$\implies \sf{2x - y = -1}$

$\implies \sf{2(y - 6) - y = -1}$

(Put the value of x From the First Condition)

$\implies \sf{2y - 12 -y = - 1}$

$\implies \sf{y = - 1 + 12}$

$\implies \boxed{\sf{y = 11}}$

Now Put the Value of y in First Condition :-

$\implies \sf{x = y - 6}$

$\implies \sf{x = 11 - 6}$

$\implies \boxed{\sf{x = 5}}$

Therefore,

$\boxed{\bold{\purple{The \ Fraction \ = \dfrac{x}{y} = \dfrac{5}{11}}}}$

$\rule{200}2$

Answer 2

${\purple{\underline{\underline{\huge{\mathtt{Answer:}}}}}}$

Given:

We have been given that the numerator of a fraction is 6 less than the denominator. If 1 is added to both numerator and denominator, it becomes half.

To Find:

We need to find the fraction.

Solution:

Let the numerator be x and denominator be y.

So, the fraction is x/y.

According to the question,

The numerator of the fraction is 6 less

than the denominator, so

x = y - 6_________(1)

Now, it is also given that if 1 is added to both numerator and denominator, it becomes half,

So, the numerator becomes (x + 1) and denominator becomes (y + 1).

=> (x + 1)/(y + 1) = 1/2

=> 2(x + 1) = 1(y + 1)

=> 2x + 2 = y + 1

=> 2x - y + 2 = 1

=> 2x - y = 1 - 2

=> 2x - y = -1_______(2)

Substituting the value of x from equation 1 in equation 2 we have,

2(y - 6) - y = -1

=> 2y - 12 - y = -1

=> y - 12 = -1

=> y = -1 + 12

=> y = 11__________(3)

Now, substituting the value of y from equation 3 in equation 1 we have,

x = y - 6

=> x = 11 - 6

=> x = 5

Therefore numerator is 5 and denominator is 11.

Hence, the fraction is 5/11.