Question

Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7 when the denominator is increased by 4.​

Answer 1

Answer :

$\underline{\boxed{\sf{Fraction\: =\:\frac{28}{45}}}}$

Step-by-step explanation :

Let the numerator be N and denominator by D.

$\implies\:\sf{Fraction\:=\:\dfrac{Numerator}{Denominator}\:=\:\dfrac{N}{D}}$

If numerator is increased by 2 then the fraction becomes 2/3.

As said in question, we have to add 2 in numerator i.e. N not in denominator.

According to question,

$\longrightarrow\:\sf{\dfrac{N+2}{D}\:=\:\dfrac{2}{3}}$

Cross-multiply them

$\longrightarrow\:\sf{3(N+2)\:=\:2(D)}$

$\longrightarrow\:\sf{3N\:+\:6\:=\:2D}$ ___(eq 1)

If denominator is increased by 4 then the fraction becomes 4/7

According to question,

$\longrightarrow\:\sf{\dfrac{N}{D+4}\:=\:\dfrac{4}{7}}$

Cross-multiply them

$\longrightarrow\:\sf{7(N)\:=\:4(D+4)}$

$\longrightarrow\:\sf{7N\:=\:4D\:+\:16}$

$\longrightarrow\:\sf{7N\:-\:16\:=\:4D}$ ___(eq 2)

Multiply (eq 1) with 2 then the equation becomes

$\longrightarrow\:\sf{6N\:+\:12\:=\:4D}$ ___(eq 3)

On comparing (eq 2) and (eq 3) we get,

$\rightarrow\:\sf{6N\:+\:12\:=\:7N\:-\:16}$

$\rightarrow\:\sf{7N\:-\:6N\:=\:12\:+\:16}$

$\rightarrow\:\sf{N\:=\:28}$

Substitute value of N = 28 in (eq 1)

$\rightarrow\:\sf{3(28)\:+\:6\:=\:2D}$

$\rightarrow\:\sf{84+6\:=\:2D}$

$\rightarrow\:\sf{90\:=\:2D}$

$\rightarrow\:\sf{D\:=\:45}$

Therefore, fraction = 28/45

Answer 2

Question :--- Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7 when the denominator is increased by 4. ?

Solution :----

Lets assume that our original Fraction is N / D ...

✪✪ Case 1 ✪✪

→ it has been said that, when numerator is increased by 2 the Fraction becomes 2/3 .

So,

→ (N+2) / D = 2/3

Cross - Multiply ,

→ 3N + 6 = 2D

→ 2D - 3N = 6 ----------------------------------- Equation (1)

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✪✪ Case 2 ✪✪

→ it has been said that, when Denominator is increased by 4 the Fraction becomes 4/7 .

So,

→ N/(D+4) = 4/7

Cross - Multiply ,

→ 7N = 4D + 16

→ 7N - 4D = 16 ------------------------------------ Equation (2)

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Multiply Equation (1) now, by 2 , and than adding that in Equation (2) we get,

→ 2(2D - 3N) + (7N - 4D) = 2*6 + 16

→ 4D - 4D - 6N + 7N = 12 + 16

→ N = 28 .

Putting This value in Any Equation now, we get,

→ 2D - 3*28 = 6

→ 2D = 6 + 84

→ 2D = 90

→ D = 45.

Hence , The required Original Fraction N/D is 28/45.