Question

the denominator of a fraction is 5 more than the numerator.if 1 is subtracted from the numerator,the result is 1/3'

Answer 1

Correct Question

The denominator of a fraction is 5 more than the numerator.if 1 is subtracted from the numerator,then the fraction become 1/3. Find the fraction.

Find out

Find the fraction.

Solution

★ Let the numerator be x then its denominator be (x + 5).

According to the given condition

✞ Denominator of a fraction is 5 more than the numerator.if 1 is subtracted from the numerator,then the fraction become 1/3.

$\implies\tt \dfrac{(x-1)}{(x+5)}=\dfrac{1}{3} \\ \\ \\ \implies\tt 3(x-1)=(x+5) \\ \\ \\ \implies\tt 3x - 3=x + 5 \\ \\ \\ \implies\tt 3x-x=5+3 \\ \\ \\ \implies\tt 2x=8 \\ \\ \\ \implies\tt x=\cancel\dfrac{8}{2}=4$

Hence,

• Required fraction

• $\tt \dfrac{Numerator}{denominator}=\dfrac{x}{(x+5)}=\dfrac{4}{9}$

$\rule{200}3$

Answer 2

Step-by-step explanation:

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

• The denominator is 5 more than the numerator

• If 1 is subtracted from the numerator the result becomes $\frac{1}{3}$

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

• The fraction ( The numerator and the denominator)

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

Let the numerator be x

According to the question :-

The denominator = x + 5

If 1 is subtracted from the numerator

The numerator is x - 1

Therefore:-

$\frac{x - 1}{x + 5} = \frac{1}{3}$

By cross multiplication:-

$\implies3(x - 1) = 1(x + 5) \\ \\ \implies3x - 3 = x + 5$

Sending the 'x' terms to The L.H.S and the constant terms to R.H.S we get:-

$3x - x = 5 + 3 \\ \\ \implies2x = 8 \\ \\ \implies x = \frac{8}{2} \\ \\ \implies x = 4$

Therefore:-

The numerator = x = 4

The denominator = x+5 = 4+5 = 9

Hence:-

$\boxed{The\:fraction \: = \frac{4}{9}}$