Question

the numerator of a fraction is 3 less that its denominator. if the numerator is made three times and 20 is added to the denominator the fraction becomes 1/8, what is the fraction?

Answer 1

Given :

The numerator of a fraction is 3 less than its denominator. If the numerator is made three times and 20 is added to the denominator the fraction becomes 1⁄8.

To Find :

What is the fraction?

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• Let us assume, that the denominator and numerator of the fraction is x and x - 3 respectively.

Original fraction :

⇢ x - 3/x

According to the question,

• When numerator is three times itself and 20 is added to the denominator, the fraction becomes 1⁄8.

∴ 3(x - 3)/x + 20 = 1⁄8

⇒ 3x - 9/x + 20 = 1⁄8

⇒ 8(3x - 9) = 1(x + 20)

⇒ 24x - 72 = x + 20

⇒ 24x - x = 20 + 72

⇒ 23x = 92

⇒ x = 92⁄23

⇒ x = 4

Therefore, the fraction is :

⟼ x - 3/x

⟼ 4 - 3/4

⟼ 1⁄4

Answer 2

$\rm{ \bf \: The \: fraction \: is \: \dfrac{1}{4} }$

Step-by-step explanation:

★Given -

• The numerator of a fraction is 3 less that its denominator.
• If the numerator is made three times and 20 is added to the denominator the fraction becomes 1/8.

★To find -

• The fraction.

★Concept -

• Here, we'll use the concept of linear equations in two variables to solve the question. Let's do it!!

★Solution -

$\rm{Let \: the \: fraction \: be \: \bf\dfrac{x}{y} }$

According to the first statement,

$\longmapsto \rm{ \bf \orange{x + 3 = y} \: \: \: \: \: \: \: \: \: (1)}$

Now, according to the second statement,

$\longmapsto \rm{ \bf\dfrac{3x}{y + 20} = \dfrac{1}{8} }$

$\longmapsto \rm{ \bf3x \times 8 = y + 20}$

$\longmapsto \rm{ \bf24x = y + 20}$

${ \longmapsto \rm{ \bf24x = x + 3 + 20 \: \: \: \: \: \: \{from \: (1) \}}}$

${ \longmapsto \rm{ \bf24x = x + 23}}$

${ \longmapsto \rm{ \bf24x - x= 23}}$

${ \longmapsto \rm{ \bf23x= 23}}$

${ \longmapsto \rm{ \bf \: x= \dfrac{ \cancel{23} \: ^{1} }{ \cancel{23} \: ^{1} }}}$

${ \longmapsto \rm{ \bf \green{ x= 1}} \: \: \: \: \:\: \: \: \: \:\:\:\:\:\: \: \{putting \: in \: (1) \}}$

$\longmapsto \rm{ \bf1 + 3 = y}$

$\longmapsto \rm{ \bf \pink{4= y}}$

$\rm{ \bf\blue{∴ the \: fraction \: is \: \dfrac{1}{4} }}$