Question

the denominator of a fraction is 3 more than the numerator if 11 is added to both the parts then the resulting fraction will be 6/7 find the numerator and the denominator

Answer 1

Given :-

• The denominator of a fraction is 3 more than the numerator if 11 is added to both the parts then the resulting fraction will be 6/7

To find :-

• Numerator and denominator

Solution :-

Let the numerator be x

As per given condition

Denominator of a fraction is 3 more than the numerator

• Denominator = x + 3

It is also given that if 11 is added to both the parts then the resulting fraction will be 6/7

According to question

→ x + 11/x + 3 + 11 = 6/7

→ x + 11/x + 14 = 6/7

→ 7(x + 11) = 6(x + 14)

→ 7x + 77 = 6x + 84

→ 7x - 6x = 84 - 77

→ x = 7

Hence,

• Numerator = x = 7

• Denominator = x + 3 = 10

Answer 2

Given : the denominator of a fraction is 3 more than the numerator if 11 is added to both the parts then the resulting fraction will be 6/7.

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Solution :

Let the numerator be x and denominator be x + 3

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies \sf \dfrac{x + 11}{x + 3 + 11} = \dfrac{6}{7}$

$:\implies \sf \dfrac{x + 11}{x + 14} = \dfrac{6}{7}$

$:\implies \sf (x + 11)7= 6(x + 14)$

$:\implies \sf 7x + 77 = 6x + 84$

$:\implies \sf 7x - 6x= 84 - 77$

$:\implies\underline{ \boxed{\sf x = 7}} \: \: \: \: \: \bigg \lgroup \bf{ Required \: Numerator} \bigg \rgroup$

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$\large\dag\: \underline{\tt Therefore,}$

$\bullet\:\:\textsf{Numerator = x = \textbf{7}}$

$\bullet\:\:\textsf{Denominator = x + 3 = 7 + 3 = \textbf{10}}$