Question

The numerator of fraction is 1 less than its denominator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5 .What is the original fraction? ? please help me....​

Answer 1

Answer:

Step-by-step explanation:

Let the denominator be x

The numerator be (x-1)

So the original fraction =x-1/x

According to the question,

(x-1)+4/x+5=4/5

x+3/x+5=4/5

4(x+5)=5(x+3)

4x+20=5x+15

5x-4x=20-15

x = 5 (the denominator)

x - 1 = 5 - 1 = 4 (the numerator)

Hence the fraction is 4/5

Answer 2

Correct Question :

The numerator of fraction is 1 less than its denominator . If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5 .What is the original fraction ?

Given :

• The numerator of fraction is 1 less than its denominator.
• If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5.

To find :

• The original fraction.

Solution :

Let the numerator of the fraction be x and the denominator of the fraction be y .

According to 1st condition :-

$\implies\sf{x=y-1................eq(1)}$

According to 2nd condition :-

$\implies\sf{\dfrac{x+4}{y+5}=\dfrac{4}{5}}$

Put x = y-1 from eq(1).

$\implies\sf{\dfrac{y-1+4}{y+5}=\dfrac{4}{5}}$

$\implies\sf{\dfrac{y+3}{y+5}=\dfrac{4}{5}}$

$\implies\sf{5y+15=4y+20}$

$\implies\sf{5y-4y=20-15}$

$\implies\sf{y=5}$

• Denominator = 5

Now put y = 5 in eq(1) for getting the value of x.

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

$\implies\sf{x=5-1}$

$\implies\sf{x=4}$

• Numerator = 4

We know,

${\boxed{\bold{Fraction=\dfrac{Numerator}{Denominator}}}}$

Therefore,

$\sf{Original\: Fraction=\dfrac{4}{5}}$

_____________________