Question

7 po
10. The denominator of a fraction is 4 more than the numerator. If 2' is added to
the numerator the fraction becomes 5/7, then the original fraction is
a) 7/11
b) 2/6
c) 5/9
d) 3/7

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Answer 1

GIVEN:-

• The denominator of a fraction is 4 more than the numerator.

• If 2' is added to
• the numerator the fraction becomes 5/7

TO FIND:-

• Then the original fraction is

Now,

$\text{Let the Numerator be "x"}$

Atq

$\text{Denominator = x + 4}$

$\rm{Original\:Fraction =\dfrac{x}{x + 4}}$

Atq.

• If 2' is added to the numerator the fraction becomes 5/7

$\text{.Numerator = x + 2}$

$\text{ Denominator = x + 4}$

$\rm{ New\:Fraction = \dfrac{5}{7}}$

$\rm{\dfrac{x+2}{x+4} =\dfrac{5}{7}}$

• Cross Multiplication method.

$\text{ 7(x+2) = 5(x+4)}$

$\text{ 7x + 14 = 5x + 20}$

$\text{ 2x = 6 }$

$\rm{ x =\dfrac{6}{2}}$

$\text{ x = 3}$

• Now Put the value of x in Original Fraction.

$\rm{Original\:Fraction =\dfrac{x}{x + 4}}$

$\rm{ Original\:Fraction = \dfrac{3}{3 + 4}}$

$\rm{ Original\:Fraction = \dfrac{3}{7}}$

Hence, Option "D" is Correct.

Answer 2

Given :

• The denominator of a fraction is 4 more than the numerator.
• If 2 is added to the numerator the fraction becomes 5/7.

To Find :

• The original fraction.

Solution :

$\longmapsto\tt\bold{Let\:the\:Numerator=y}$

As the denominator of a fraction is 4 more than the numerator. So ,

$\longmapsto\tt\bold{Denominator=y+4}$

Now :

If 2 is added to the numerator then the fraction becomes 5/7 .So,

$\longmapsto\tt{Numertor=y+2}$

A.T.Q :

$\longmapsto\tt{\dfrac{y+2}{y+4}=\dfrac{5}{7}}$

$\longmapsto\tt{7(y+2)=5(y+4)}$

$\longmapsto\tt{7y+14=5y+20}$

$\longmapsto\tt{7y-5y=20-14}$

$\longmapsto\tt{2y=6}$

$\longmapsto\tt{y=\cancel\dfrac{6}{2}}$

$\longmapsto\tt\bold{y=3}$

Therefore :

$\longmapsto\tt\bold{Numerator=3}$

$\longmapsto\tt{Denominator=3+4}$

$\longmapsto\tt\bold{7}$

So , The Original fraction is 3/7....

Option d) 3/7 is correct...