Question

21. The denominator of a fraction is greater than its numerator by 11. If 8 is
added to both its numerator and denominator, it becomes
Find the
4
fraction.
3​

Answer 1

${\huge {\sf {\bf {\underline {\blue {Correct~ Question}}}}}}$

The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes ${\sf {\dfrac {3}{4}}}$ . Find the fraction.

${\huge {\sf {\bf {\underline {\blue {Answer}}}}}}$

Given :-

• The denominator of a fraction is greater than its numerator by 11.

• If 8 is added to both its numerator and denominator, it becomes ${\sf {\dfrac {3}{4} }}$

To Find :-

• The fraction.

Solution :-

$\rightsquigarrow$ Let, the numerator be "x"

$\rightsquigarrow$ and the denominator be "y"

$\rightsquigarrow$ Hence, the fraction is ${\sf {\dfrac {x}{y}}}$ .

Now, according to the question

The denominator of a fraction is greater than its numerator by 11.

$\implies {\sf {y = x + 11}}$ -------------- eq. ( i )

If 8 is added to both its numerator and denominator, it becomes ${\sf {\dfrac {3}{4}}}$ .

$\implies {\sf {\dfrac {x + 8}{y + 8}} = {\dfrac {3}{4}} }$

$\implies {\sf {4 (x + 8) = 3 (y + 8)} }$

$\implies {\sf {4x + 32 = 3y + 24}}$

$\implies {\sf {4x - 3y = 24 - 32}}$

$\implies {\sf {4x - 3y = -8}}$ ---------------- eq. ( ii )

Now, substitute the value of "y" from eq. ( i ) to eq. ( ii )

$\implies {\sf {4x - 3y = -8}}$

$\implies {\sf {4x - 3(x + 11) = -8}}$

$\implies {\sf {4x - 3x - 33 = -8}}$

$\implies {\sf {x = -8 + 33}}$

$\implies {\underline {\boxed {\sf {x = 25}}}}$

Substitute the value of "x" in eq. ( i )

$\implies {\sf {y = x + 11}}$

$\implies {\sf {y = 25 + 11}}$

$\implies {\underline {\boxed {\sf {y = 36}}}}$

Therefore, the fraction is $\implies {\underline {\boxed {\sf {\dfrac {x}{y}} = {\dfrac {25}{36}}}}}$

Answer 2

Answer:

This is the answer

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