Question

Find the numerator
The numerator of a fraction is larger than its denominator by 4. If we add 1 to its
denominator, the fraction becomes. Find the fraction.
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Answer 1

Appropriate Question :

⇒The numerator of a fraction is larger than its denominator by 4. If we add 1 to its  denominator, the fraction becomes 3/2 . Find the fraction.

Given,

• The Numerator of a fraction is larger than its denominator by 4.
• When we add 1 to its denominator then the fraction becomes 3/2

To Find,

• The fraction

Solution,

⇒Suppose the numerator be x

And, Suppose the denominator be y

$\bold{\underline{\green{According \ to \ the \ First \ Condition :}}}$

• The Numerator of a fraction is larger than its denominator by 4.

$\implies \boxed{\sf{x = y + 4}}$

$\bold{\underline{\green{According \ to \ the \ Second \ Condition :}}}}$

• When we add 1 to its denominator then the fraction becomes 3/4.

$\implies \sf{\dfrac{x}{y + 1} = \dfrac{3}{2}}$

$\implies \sf{2x = 3(y + 1)}$

$\implies \sf{2x = 3y + 3}$

$\implies \sf{2x - 3y = 3 }$

$\implies \sf{2(y + 4) - 3y = 3}$

(Put the value of x From the Equation First)

$\implies \sf{2y + 8 -3y = 3}$

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

$\implies \boxed{\sf{y = \df{5}}}$

Now Put the value of y in First Condition :-

$\implies \sf{x = y + 4}$

$\implies \sf{x = 5 + 4}$

$\implies \boxed{\sf{x = 9}}$

Therefore,

$\boxed{\sf{\purple{The \ Fraction = \dfrac{x}{y} = \dfrac{9}{5}}}}$

$\rule{200}2$

Answer 2

Answer:-

Let the fraction be x/y.

Given:

The numerator is larger than the denominator by 4.

=> x = y + 4 -- equation (1)

And,

If 1 is added to denominator , the fraction becomes 3/2.

According to the question,

$\frac{x}{y +1 } = \frac{3}{2}$

Substitute "x" value here.

$\frac{y + 4}{y + 1} = \frac{3}{2}$

After cross multiplication we get,

$2(y + 4) = 3(y + 1) \\ \\ 2y + 8 = 3y + 3 \\ \\ 2y - 3y = 3 - 8 \\ \\ - y = - 5 \\ \\ y = 5$

Substitute "y" value in equation (1)

x = y + 4

x = 5 + 4

x = 9

Therefore, the fraction x/y = 9/5.