Question

The numerator of a fraction is 1 less than the denominator.if numerator is decreased by two and denominator is increased by 3the fraction becomes 1/4. What is the fraction

Answer 1

Given,

• The numerator of fraction is 1 less than the denominator .
• denominator both are increased by 3 and numerator decreased by two so the fraction become 1/4 .

To Find,

• The Fraction

Solution,

⇒Suppose the denominator be x

So , numerator be (x - 1)

According to the Question :

$\implies \bold{\frac{x - 1 - 2}{x + 3} = \frac{1}{4}}$

$\implies \bold{\frac{x - 3}{x + 3} = \frac{1}{4}}$

$\implies \bold{4( x - 3) = 1( x +3)}$

$\implies \bold{4x - 12 = x +3}$

$\implies \bold{4x - x = 3 + 12}$

$\implies \bold{3x = 15}$

$\implies \boxed{\bold{x = 5}}$

Now Find the fraction :-

$\implies \bold{\frac{x - 1}{x}}$

$\implies \bold{\frac{5 - 1}{5}}$

$\implies \boxed{\bold{\red{\frac{4}{5}}}}$

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Answer 2

$\tt{\huge{\pink{Hello!!! }}}$

Given Fraction :

$\tt{ \purple{ \leadsto{ \sf{ \dfrac{x}{y} }}}}$

$\tt{ \orange{ \leadsto{x \: = y - 1}}}$

Hence the Fraction is :

$\tt{ \blue{ \leadsto{ \sf{ \dfrac{y - 1}{y} }}}}$

Now the numerator is decreased by two and the denominator is increased by 3.

$\tt{ \red{ \leadsto{ \sf{ \dfrac{y - 3}{y + 3} = \dfrac{1}{4} }}}}$

$\tt{ \green{ \leadsto{ \sf{ 4y - 12 = y + 3 }}}}$

$\tt{ \purple{ \leadsto{ \sf{ y \: = 5 }}}}$

$\tt{ \orange{ \leadsto{ \sf{fraction \: becomes \: \dfrac{4}{5} }}}}$