Question

The denominator of a fraction is greater than the numerator by 3. If 7 is added to the
numerator, the fraction increases by unity. Find the fraction.
​

Answer 1

Answer :-

$\sf{Fraction\:=\:\dfrac{4}{7}}$

____________________

Let the -

• numerator be M.
• denominator = N.

The denomination of a fraction is greater than the numerator by 3.

Then,

$\implies\sf{N\: = \:M\: + \:3}$ ...(1)

If 7, is added to the numerator then the fraction increased by unity.

Now,

$\bold{If\:7\:is\:added\:to\:numerator}=> \begin{cases} \sf{Numerator = M + 7} \end{cases}$

7 is added to numerator only, not in the denomination. Means, the denominator is the same i.e. M + 3

According to question,

$\implies\:\sf{\dfrac{M}{M\:+\:3}\:=\:\dfrac{M\:+\:7}{M\:+\:3}\:+\:1}$

$\implies\:\sf{\dfrac{M}{M\:+\:3}\:-\:\dfrac{M\:+\:7}{M\:+\:3}\:=\:1}$

$\implies\:\sf{\dfrac{M\:-\:M\:+\:7}{M\:+\:3}\:=\:1}$

$\implies\:\sf{7\:=\:M\:+\:3}$

$\implies\:\sf{M\:=\:4}$

Substitute value of M in (1)

$\implies\:\sf{N\:=\:3\:+\:4}$

$\implies\:\sf{N\:=\:7}$

•°• Fraction = $\bold{\sf{\dfrac{Numerator}{Denominator}}}$

$\implies\:\sf{\dfrac{M}{N}\:=\:\dfrac{4}{7}}$

Answer 2

Answer:

Step-by-step explanation:

Answer :-

____________________

Let the -

numerator be M.

denominator = N.

The denomination of a fraction is greater than the numerator by 3.

Then,

...(1)

If 7, is added to the numerator then the fraction increased by unity.

Now,

7 is added to numerator only, not in the denomination. Means, the denominator is the same i.e. M + 3

According to question,

Substitute value of M in (1)

•°• Fraction =